robust output regulation of t s fuzzy systems with multiple time varying state and input delays this paper proposes a robust output regulator design for takagi sugeno t s fuzzy systems with uncertain time delays for generalization of the control problem we assume that there exist affine dynamics unknown multiple time varying delays in state and input uncertain parameters disturbance and partial state feedback both continuous time and discrete time cases are considered in a unified theoretical derivation here we introduce a memoryless fuzzy observer and a fuzzy integral compensator in comparison with previous studies the proposed scheme drops the need for coordinate transformation calculation of the desired operational point which is known state and input delays and exact fuzzy modeling the control result is asymptotic output regulation for systems without disturbance and guaranteed h infin performance for systems with disturbance moreover a piecewise constant output regulation is achieved without controller redesign in addition the developed fuzzy regulator can be applied to both affine and nonaffine uncertain time delay systems finally numerical simulations are performed by using two typical time delay systems to validate the expected performance

lattice boltzmann model for the incompressible navier stokes equation in this paper a lattice boltzmann lb model to simulate incompressible flow is developed the main idea is to explicitly eliminate the terms of o m2 where m is the mach number due to the density fluctuation in the existing lb models in the proposed incompressible lb model the pressure p instead of the mass density is the independent dynamic variable the incompressible navier stokes equations are derived from the incompressible lb model via chapman enskog procedure numerical results of simulations of the plane poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2d womersley flow are presented the numerical results are found to be in excellent agreement with theory

an approximate a algorithm and its application to the scs problem in this paper we deal with algorithm a and its application to the problem of finding the shortest common supersequence of a set of sequences a is a powerful search algorithm which may be used to carry out concurrently the construction of a network and the solution of a shortest path problem on it we prove a general approximation property of a which by building a smaller network allows us to find a solution with a given approximation ratio this is particularly useful when dealing with large instances of some problem we apply this approach to the solution of the shortest common supersequence problem and show its effectiveness

stabilizing controller design for uncertain nonlinear systems using fuzzy models a lyapunov based stabilizing control design method for uncertain nonlinear dynamical systems using fuzzy models is proposed the controller is constructed using a design model of the dynamical process to be controlled the design model is obtained from the truth model using a fuzzy modeling approach the truth model represents a detailed description of the process dynamics the truth model is used in a simulation experiment to evaluate the performance of the controller design a method for generating local models that constitute the design model is proposed sufficient conditions for stability and stabilizability of fuzzy models using fuzzy state feedback controllers are given the results obtained are illustrated with a numerical example involving a four dimensional nonlinear model of a stick balancer

finite element lattice boltzmann simulations of free surface flow in a concentric cylinder the annular centrifugal contactor is a compact mixer centrifuge device designed for liquid liquid extraction operations in processes for recycling nuclear fuel the flow in the annulus of a centrifugal contactor is similar to the taylor vortex flow with superimposed axial flow the major differences are that the contactor has one end that is open to air and the free surface effects dominate the annular flow in this study we demonstrate the application of a finite element lattice boltzmann equation fe lbe method to the annular mixing geometry as found in a centrifugal contactor the computational results are validated with available experimental observations with the reynolds number re in the range of 1250

robust h sub spl infin control for fuzzy systems with frobenius norm bounded uncertainties in this paper we investigate the problem of robust h sub spl infin performance and stabilization for a class of uncertain fuzzy systems with frobenius norm bounded parameter uncertainties in all system matrices both continuous and discrete time uncertain fuzzy systems are considered under a unified treatment called bounded real lemma for fuzzy systems unlike the bounded real lemma in the linear theory of robust h sub spl infin control where necessary and sufficient conditions were obtained only sufficient condition based on lyapunov method is shown furthermore connection between robust h sub spl infin problems involving uncertainty and standard uncertainty free h sub spl infin problems is established via matrix algebra as for controller synthesis a state feedback fuzzy control law is designed via relaxed linear matrix inequality lmi formulations

static output feedback h control of a class of nonlinear discrete time systems this paper is concerned with the problem of designing robust h static output feedback sof controllers for a class of discrete time nonlinear systems which are represented by t s fuzzy models by considering the properties of system output matrices a method for h sof control synthesis is developed in terms of solutions to a set of linear matrix inequalities lmis in contrast to the existing techniques for designing sof controllers the new proposed method can give less conservative results by removing the constraint that the considered lyapunov matrix is diagonal numerical examples are given to illustrate the effectiveness of the proposed design method

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

steady state convergence acceleration of the generalized lattice boltzmann equation with forcing term through preconditioning several applications exist in which lattice boltzmann methods lbm are used to compute stationary states of fluid motions particularly those driven or modulated by external forces standard lbm being explicit time marching in nature requires a long time to attain steady state convergence particularly at low mach numbers due to the disparity in characteristic speeds of propagation of different quantities in this paper we present a preconditioned generalized lattice boltzmann equation glbe with forcing term to accelerate steady state convergence to flows driven by external forces the use of multiple relaxation times in the glbe allows enhancement of the numerical stability particular focus is given in preconditioning external forces which can be spatially and temporally dependent in particular correct forms of moment projections of source forcing terms are derived such that they recover preconditioned navier stokes equations with non uniform external forces as an illustration we solve an extended system with a preconditioned lattice kinetic equation for magnetic induction field at low magnetic prandtl numbers which imposes lorentz forces on the flow of conducting fluids computational studies particularly in three dimensions for canonical problems show that the number of time steps needed to reach steady state is reduced by orders of magnitude with preconditioning in addition the preconditioning approach resulted in significantly improved stability characteristics when compared with the corresponding single relaxation time formulation

some progress in lattice boltzmann method part i nonuniform mesh grids a new lattice boltzmann algorithm is proposed to simulate the navier stokes equation on arbitrary nonuniform mesh grids the new algorithm retains the advantages of the lattice boltzmann method parallel of algorithm ease of programming and ability to incorporate microscopic interactions a simulation of flow in a two dimensional symmetric channel with sudden expansion is carried out using the new algorithm on a nonuniform mesh the results of the simulation are in excellent agreement with previous experimental and numerical results

robustness design of nonlinear dynamic systems via fuzzy linear control this study introduces a fuzzy linear control design method for nonlinear systems with optimal h sup spl infin robustness performance first the takagi and sugeno fuzzy linear model 1985 is employed to approximate a nonlinear system next based on the fuzzy linear model a fuzzy controller is developed to stabilize the nonlinear system and at the same time the effect of external disturbance on control performance is attenuated to a minimum level thus based on the fuzzy linear model h sup spl infin performance design can be achieved in nonlinear control systems in the proposed fuzzy linear control method the fuzzy linear model provides rough control to approximate the nonlinear control system while the h sup spl infin scheme provides precise control to achieve the optimal robustness performance linear matrix inequality lmi techniques are employed to solve this robust fuzzy control problem in the case that state variables are unavailable a fuzzy observer based h sup spl infin control is also proposed to achieve a robust optimization design for nonlinear systems a simulation example is given to illustrate the performance of the proposed design method

observer based relaxed cal h _ infty control for fuzzy systems using a multiple lyapunov function this short paper proposes a method of designing a fuzzy observer based h infin controller for discrete time takagi sugeno t s fuzzy systems to enhance the applicability of the output feedback controller and improve its performance this short paper first builds a set of fuzzy control rules with premise variables different from those of the t s fuzzy system and sets the overall controller to be dependent on not only the current time but also the one step past information on the estimated fuzzy weighting functions then based on the fuzzy control rules this short paper establishes a less conservative h infin stabilization condition incorporated with a multiple lyapunov function dependent on the estimated fuzzy weighting functions through a two step design procedure the h infin stabilization condition is formulated in terms of parameterized linear matrix equalities plmis which are reconverted into lmis with the help of an efficient and effective relaxation scheme

a finite difference lattice boltzmann method with second order accuracy of time and space for incompressible flow abstract in this paper a kind of finite difference lattice boltzmann method with the second order accuracy of time and space t2s2 fdlbm is proposed in this method a two stage time accurate discretization approach is applied to construct time marching scheme and the spatial gradient operator is discretized by a mixed difference scheme to maintain a second order accuracy in space it is shown that the previous finite difference lattice boltzmann method fdlbm guo and zhao 2003 is a special case of the t2s2 fdlbm through the von neumann analysis the stability of the method is analyzed and two specific t2s2 fdlbms are discussed the two t2s2 fdlbms are applied to simulate some incompressible flows with the non uniform grids compared with other high order fdlbms this two t2s2 fdlbms keep the simplicity of standard lattice boltzmann method compared with the previous fdlbm and lattice boltzmann method the two t2s2 fdlbms are more accurate and more stable the value of the courant friedrichs lewy condition number in our method can be up to 0 9 which also significantly improves the computational efficiency

a novel observer based output feedback controller design for discrete time fuzzy systems this paper addresses the problem of observer based output feedback controller designs for discrete time t s fuzzy systems based on a relaxed approach in which the fuzzy lyapunov functions are used different from the existing two step method a single step linear matrix inequality method is provided for the observer based controller design it is shown that the controller and observer parameters can be obtained by solving a set of strict linear matrix inequalities that are numerically feasible with commercially available software the new design method not only overcomes the drawback induced by the two step approach but also provides less conservative results over some existing results finally the effectiveness of the proposed approach is demonstrated by an example

output stabilization of takagi sugeno fuzzy systems abstract in this paper the output stabilization problem of takagi sugeno fuzzy models is considered first a natural form of observers for such models is given sufficient conditions for their asymptotic convergence are given which are dual to those for the stability of state feedback fuzzy controllers we then show that a state feedback controller and an observer always yield a stabilizing output feedback controller provided that the stabilizing property of the control and the asymptotic convergence of the observer are guaranteed by the lyapunov method using positive definite matrices in this sense it is shown that the separation principle holds for takagi sugeno fuzzy systems two design examples are given to illustrate the theory

robust h control of takagi sugeno fuzzy systems with state and input time delays this paper addresses the robust h fuzzy control problem for nonlinear uncertain systems with state and input time delays through takagi sugeno t s fuzzy model approach the delays are assumed to be interval time varying delays and no restriction is imposed on the derivative of time delay based on lyapunov krasoviskii functional method delay dependent sufficient conditions for the existence of an h controller are proposed in linear matrix inequality lmi format illustrative examples are given to show the effectiveness and merits of the proposed fuzzy controller design methodology

finite volume lattice boltzmann method we present a finite volume formulation for the lattice boltzmann method fvlbm based on standard bilinear quadrilateral elements in two dimensions the accuracy of this scheme is demonstrated by comparing the velocity field with the analytical solution of the navier stokes equations for time dependent rotating couette flow and taylor vortex flow to demonstrate the flexibility of the scheme we have also simulated a modified rotating couette flow where the inner cylinder has an elliptical shape the results agree with those obtained from the traditional marker and cell method the fvlbm scheme is applicable to arbitrarily shaped two dimensional regions and thus the range of applicability of the lattice boltzmann method has been significantly extended

reliable rm h_infty fuzzy control for continuous time nonlinear systems with actuator failures this paper is concerned with the design of reliable hinfin fuzzy controllers for continuous time nonlinear systems with actuator failures the takagi and sugeno fuzzy model is employed to represent a nonlinear system the objective is to find a stabilizing state feedback fuzzy controller such that the nominal hinfin performance is optimized while satisfying a prescribed hinfin performance constraint in the actuator failure cases based on the linear matrix inequality lmi techniques two efficient methods for the design of a suboptimal reliable hinfin fuzzy controller are proposed different lyapunov functions are used during the design for the nominal and actuator failure cases which lead to a less conservative controller design in the first method a single lyapunov function is used for the actuator failure cases the second method adopts a parameter dependent lyapunov function for the actuator failure cases which further reduces the conservatism of the design finally numerical simulations on the chaotic rossler system are given to illustrate the effectiveness of the proposed design methods

semi implicit linearized multiple relaxation time formulation of lattice boltzmann schemes for mixture modeling a lattice boltzmann model for mixture modeling is developed by applying the multiple relaxation time mrt approach to the hamel model which allows one to derive from a general framework different model equations independently proposed like the gross krook model and the sirovich model by imposing some physical constraints the mrt lattice boltzmann hamel model reduces to the generalized mrt lattice boltzmann gross krook model involving the local maxwellian centered on the barycentric velocity which allows one to tune independently the species diffusivity the mixture kinematic viscosity and the mixture bulk viscosity reducing the number of moving particles over the total is possible to deal effectively with mass particle ratios far from unity and for this reason to model the pressure driven diffusion a convenient numerical approach is proposed for solving the developed model which essentially widens the stability range of conventional schemes in terms of dimensionless relaxation frequencies by solving explicitly the advection operator together with the nonlinear terms of the collisional operator and solving implicitly the residual linear terms in this way the calculations are drastically reduced and the operative matrices can be computed once for all at the beginning of the calculation implying moderate additional computational demand following this approach a semi implicit linearized backward euler scheme ideal for parallel implementations is proposed in order to achieve the previous results the asymptotic analysis recently suggested for analyzing the macroscopic equations corresponding to lattice boltzmann schemes in the low mach number limit proves to be an effective tool some numerical tests are reported for proving the consistency of the proposed method with both the fick model and maxwell stefan model in the macroscopic limit

robust h sub spl infin disturbance attenuation for a class of uncertain discrete time fuzzy systems the paper is concerned with robust stabilization and h sub spl infin control of a class of uncertain discrete time fuzzy systems the class of uncertain systems is described by state space takagi sugeno ts fuzzy models with linear nominal parts and norm bounded parameter uncertainties in the state and output equations first a sufficient condition on robust stability of the fuzzy models is proposed then h sub spl infin disturbance attenuation performance of the fuzzy models is analyzed some sufficient conditions are derived on robust h sub spl infin disturbance attenuation in which both robust stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainties a numerical example shows the use of the results on the stabilization and h sub spl infin disturbance attenuation of a class of discrete time nonlinear systems via fuzzy switch

singular forces and pointlike colloids in lattice boltzmann hydrodynamics we present an accurate method to include arbitrary singular distributions of forces in the lattice boltzmann formulation of hydrodynamics we validate our method with several examples involving stokeslet stresslet and rotlet singularities finding excellent agreement with analytical results a minimal model for sedimenting particles is presented using the method in the dilute limit this model has accuracy comparable to but computational efficiency much greater than algorithms that explicitly resolve the size of the particles

semi lagrangian implicit bhatnagar gross krook collision model for the finite volume discrete boltzmann method in order to increase the accuracy of temporal solutions reduce the computational cost of time marching and improve the stability associated with collisions for the finite volume discrete boltzmann method an advanced implicit bhatnagar gross krook bgk collision model using a semi lagrangian approach is proposed in this paper unlike existing models in which the implicit bgk collision is resolved either by a temporal extrapolation or by a variable transformation the proposed model removes the implicitness by tracing the particle distribution functions pdfs back in time along their characteristic paths during the collision process an interpolation scheme is needed to evaluate the pdfs at the traced back locations by using the first order interpolation the resulting model allows for the straightforward replacement of f eq n 1 by f eq n no matter where it appears after comparing the proposed model with the existing models under different numerical conditions e g different flux schemes and time marching schemes and using the proposed model to successfully modify the variable transformation technique three conclusions can be drawn first the proposed model can improve the accuracy by almost an order of magnitude second it can slightly reduce the computational cost therefore the proposed scheme improves accuracy without extra cost finally the proposed model can significantly improve the t limit compared to the temporal interpolation model while having the same t limit as the variable transformation approach the proposed scheme with a second order interpolation is also developed and tested however that technique displays no advantage over the simple first order interpolation approach both numerical and theoretical analyses are also provided to explain why the developed implicit scheme with simple first order interpolation can outperform the same scheme with second order interpolation as well as the existing temporal extrapolation and variable transformation schemes

lattice boltzmann model for exterior flows with an annealing preconditioning method in this paper we propose a highly efficient and stable lattice boltzmann method for solving low reynolds number exterior flows using a preconditioning technique the present method is based on replacing the constant preconditioning parameter gamma within uniform grids guo phys rev e 70 066706 2004 by a space and time dependent one in a nested mesh refined domain to do this for the transition from a fine to the neighboring coarser grid gamma has been divided by a factor k which is large initially and anneals stepwise to a small value after some iterations with this technique more than one order of magnitude larger convergence rate can be achieved and several orders of magnitude larger system size can be treated

observer based h_ infty sampled data fuzzy control for a class of nonlinear parabolic pde systems in this paper an observer based h infty sampled data fuzzy control problem is addressed for a class of nonlinear parabolic partial differential equation pde systems with the aid of the modal decomposition technique a nonlinear ordinary differential equation ode model is initially derived to describe the dominant slow dynamics of the pde system subsequently the resulting nonlinear ode model is accurately represented by the takagi sugeno t s fuzzy model then based on the t s fuzzy model a finite dimensional observer based sampled data fuzzy control design with h infty performance is developed for the pde system via employing a novel time dependent functional the outcome of the observer based h infty sampled data fuzzy control problem can be formulated as a bilinear matrix inequality optimization problem moreover an iterative optimization algorithm based on the linear matrix inequalities is given to obtain a suboptimal h infty sampled data fuzzy controller finally simulation results on the fisher equation and a temperature cooling fin of high speed aerospace vehicle illustrate that the proposed design method is effective

existence of similarity transformation converting bmis to lmis under a mild condition we investigate the existence of a similarity transformation regarding robust hinfin stability analysis and observer controller synthesis problems the observer based controller is capable of disturbance rejection in the presence of unknown but bounded disturbance we present results which illustrate plainly the role of the similarity transformation in converting a bmi problem into an lmi problem in a unified fashion applicable to both continuous and discrete time problems with or without uncertainty finally the validity and applicability of the approach are illuminated by examples

a stable discretization of the lattice boltzmann equation for simulation of incompressible two phase flows at high density ratio a stable discretization of the lattice boltzmann equation lbe for non ideal gases is presented for simulation of incompressible two phase flows having high density and viscosity ratios the stiffness of the discretized forcing terms in lbe for non ideal gases is known to trigger severe numerical instability and restrict practical application of the lbe method use of a proper pressure updating scheme is also crucial to the stability of the lbe method because of non negligible pressure variation across the phase interface to deal with these issues we propose a stable discretization scheme which assumes the low mach number approximation and utilizes the stress and potential forms of the surface tension force the incompressible transformation and the consistent discretization of the intermolecular forcing terms the proposed stable discretization scheme is applied to simulate 1 d advection equation with a source term a stationary droplet droplet oscillation and droplet splashing and deposition on a thin film at a density ratio of 1000 with varying reynolds numbers the numerical solutions of stationary and oscillatory droplets agree well with analytic solutions including the laplace s law the time history of the spread factor of the liquid sheet emitted after the droplet impact also follows the known spreading power law

on the approximation of shortest common supersequencesand longest common subsequences the problems of finding shortest common supersequences scs and longest common subsequences lcs are two well known bf np hard problems that have applications in many areas including computational molecular biology data compression robot motion planning and scheduling text editing etc a lot of fruitless effort has been spent in searching for good approximation algorithms for these problems in this paper we show that these problems are inherently hard to approximate in the worst case in particular we prove that i scs does not have a polynomial time linear approximation algorithm unless bf p bf np ii there exists a constant delta 0 such that if scs has a polynomial time approximation algorithm with ratio log delta n where n is the number of input sequences then bf np is contained in bf dtime 2 polylog n iii there exists a constant delta 0 such that if lcs has a polynomial time approximation algorithm with performance ratio n delta then bf p bf np the proofs utilize the recent results of arora et al proc 23rd ieee symposium on foundations of computer science 1992 pp 14 23 on the complexity of approximation problems in the second part of the paper we introduce a new method for analyzing the average case performance of algorithms for sequences based on kolmogorov complexity despite the above nonapproximability results we show that near optimal solutions for both scs and lcs can be found on the average more precisely consider a fixed alphabet sigma and suppose that the input sequences are generated randomly according to the uniform probability distribution and are of the same length n moreover assume that the number of input sequences is polynomial in n then there are simple greedy algorithms which approximate scs and lcs with expected additive errors o n 0 707 and o n frac 1 2 epsilon for any epsilon 0 respectively incidentally our analyses also provide tight upper and lower bounds on the expected lcs and scs lengths for a set of random sequences solving a generalization of another well known open question on the expected lcs length for two random sequences k alexander the rate of convergence of the mean length of the longest common subsequence 1992 manuscript v chvatal and d sankoff j appl probab 12 1975 pp 306 315 d sankoff and j kruskall eds time warps string edits and macromolecules the theory and practice of sequence comparison addison wesley reading ma 1983

analysis and design of fuzzy controller and fuzzy observer this paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the takagi sugeno t s fuzzy model the main contribution of the paper is the development of the separation property that is the fuzzy controller and the fuzzy observer can be independently designed a numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer

robust h fuzzy static output feedback control of t s fuzzy systems with parametric uncertainties this paper addresses robust h fuzzy static output feedback control problem for t s fuzzy systems with time varying norm bounded uncertainties sufficient conditions for synthesis of a fuzzy static output feedback controller for t s fuzzy systems are derived in terms of a set of linear matrix inequalities lmis in comparison with the existing literatures the proposed approach not only simplifies the design procedure but also achieves a better h performance three drawbacks existing in the previous papers such as coordinate transformation same output matrices and bmi problem have been eliminated the effectiveness of the proposed design method is demonstrated by an example for the control of a truck trailer system

chebyshev collocation spectral lattice boltzmann method for simulation of low speed flows in this study the chebyshev collocation spectral lattice boltzmann method ccslbm is developed and assessed for the computation of low speed flows both steady and unsteady flows are considered here the discrete boltzmann equation with the bhatnagar gross krook approximation based on the pressure distribution function is considered and the space discretization is performed by the chebyshev collocation spectral method to achieve a highly accurate flow solver to provide accurate unsteady solutions the time integration of the temporal term in the lattice boltzmann equation is made by the fourth order runge kutta scheme to achieve numerical stability and accuracy physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used an iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows the main advantage of using the ccslbm over other high order accurate lattice boltzmann method lbm based flow solvers is the decay of the error at exponential rather than at polynomial rates note also that the ccslbm applied does not need any numerical dissipation or filtering for the solution to be stable leading to highly accurate solutions three two dimensional 2d test cases are simulated herein that are a regularized cavity the taylor vortex problem and doubly periodic shear layers the results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement the computational efficiency of the proposed solution methodology based on the ccslbm is also examined by comparison with those of the standard streaming collision classical lbm and two finite difference lbm solvers the study indicates that the ccslbm provides more accurate and efficient solutions than these lbm solvers in terms of cpu and memory usage and an exponential convergence is achieved rather than polynomial rates the solution methodology proposed the ccslbm is also extended to three dimensions and a 3d regularized cavity is simulated the corresponding results are presented and validated indications are that the ccslbm developed and applied herein is robust efficient and accurate for computing 2d and 3d low speed flows note also that high accuracy solutions obtained by applying the ccslbm can be used as benchmark solutions for the assessment of other lbm based flow solvers

new approaches to relaxed quadratic stability condition of fuzzy control systems this paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems the first one employs the s procedure to utilize information regarding the premise parts of the fuzzy systems the next one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality the relationships between the suggested stability conditions and the conventional well known stability conditions reported in the previous literatures are also discussed and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions finally some examples and simulation results are presented to illustrate the effectiveness of the stability conditions

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

evaluation of the finite element lattice boltzmann method for binary fluid flows abstract in contrast to the commonly used lattice boltzmann method off lattice boltzmann methods decouple the velocity discretization from the underlying spatial grid thereby potentially increasing the geometric flexibility of the method the current work combines characteristic based integration of the streaming step with the free energy based multiphase model by lee and lin 2005 this allows for simulation time steps more than an order of magnitude larger than the relaxation time unlike previous work by wardle and lee 2013 that integrated intermolecular forcing terms in the advection term the current scheme applies collision and forcing terms locally for a simpler finite element formulation a series of thorough benchmark studies reveal that this does not compromise stability and that the scheme is able to accurately simulate flows at large density and viscosity contrasts

new applications of the incompressibility method part ii abstract the incompressibility method is an elementary yet powerful proof technique it has been used successfully in many areas li and vitanyi an introduction to kolmogorov complexity and its applications springer new york 1997 to further demonstrate its power and elegance we exhibit new simple proofs using the incompressibility method

fuzzy output regulator design of discrete affine systems with multiple time varying delays this paper presents a takagi sugeno t s fuzzy model based regulator for a class of discrete affine nonlinear systems with multiple time varying delays first combining the t s fuzzy representation and lyapunov krasovskii method we derive the sufficient conditions for the unforced affine system with multiple time varying delays disturbances and non vanishing bias at the origin these stability conditions are not derived in current literature next the fuzzy output regulator is proposed by introducing a memoryless fuzzy observer and a fuzzy integral compensator then asymptotic output regulation and state estimation is achieved by solving linear matrix inequalities lmis in a two step manner moreover an h performance criterion is guaranteed for disturbance attenuation compared to traditional approaches this paper does not require exact information of partial states each time varying delay and the desired operational point the proposed controller yields a multi task regulation without needing controller redesign once the output command is changed finally numerical simulations are carried out on two intuitive time delay systems to illustrate the expected performance

fuzzy state space modeling and robust observer based control design for nonlinear partial differential systems in this paper a robust fuzzy control design is proposed for the stabilization of nonlinear partial differential systems npdss based on galerkin s method a takagi sugeno t s fuzzy pds is first proposed to model an npds then the t s fuzzy pds can be represented by a finite dimensional t s fuzzy subsystem in controlled mode and a coupled infinite dimensional t s fuzzy subsystem in residual mode therefore the npds can be partitioned into a finite dimensional t s fuzzy slow state space subsystem to be controlled and a coupled infinite dimensional fast residual subsystem to be tolerated based on the small gain theorem a robust fuzzy observer based controller is developed to tolerate the coupled residual subsystem to asymptotically stabilize the npds furthermore based on the dissipative theory an hinfin control design is proposed to attenuate the effects of external disturbances and measurement noises on the robust stabilization of npdss the matlab linear matrix inequality toolbox can be employed to efficiently solve the optimal hinfin fuzzy observer based control design problem of npdss finally a simulation example is given to illustrate the design procedure and confirm the performance of the proposed robust fuzzy observer based control method for the perturbative npdss

preconditioned lattice boltzmann method for steady flows in this paper we propose a preconditioned lattice boltzmann lb method for steady incompressible flows for steady flows the macroscopic equations derived from this lb model are equivalent to those from the standard lb model but with an improved eigenvalue system the proposed model can be viewed as an explicit solver for preconditioned compressible navier stokes equations linear stability analysis is performed and the results show that the stability of the model is the same as that of the standard lb model for low mach numbers the proposed model retains the structure of the standard lb model and hence possesses all the advantages numerical tests show that the convergence rate can be enhanced as much as an order of magnitude compared to the standard lattice boltzmann method the accuracy of the solutions is improved as well

least squares finite element scheme for the lattice boltzmann method on an unstructured mesh a numerical model of the lattice boltzmann method lbm utilizing least squares finite element method in space and the crank nicolson method in time is developed this method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite element method while employing accurate least squares optimization fourth order accuracy in space and second order accuracy in time are derived for a pure advection equation on a uniform mesh while high stability is implied from a von neumann linearized stability analysis implemented on unstructured mesh through an innovative element by element approach the proposed method requires fewer grid points and less memory compared to traditional lbm accurate numerical results are presented through two dimensional incompressible poiseuille flow couette flow and flow past a circular cylinder finally the proposed method is applied to estimate the permeability of a randomly generated porous media which further demonstrates its inherent geometric flexibility

robust fuzzy h_ infty estimator based stabilization design for nonlinear parabolic partial differential systems with different boundary conditions in this paper a new robust fuzzy h infty estimator based stabilization design for a class of n dimensional nonlinear parabolic partial differential systems pdss with either the dirichlet or neumann boundary conditions is proposed first an n dimensional parabolic takagi sugeno t s fuzzy pds is used to approximate the n dimensional nonlinear parabolic pds via the knowledge based t s fuzzy system technique second based on the n dimensional parabolic t s fuzzy pds a robust fuzzy estimator based controller is employed not only to stabilize the pds but also to attenuate the effects of external and measurement noises on the pds in the spatiotemporal domain below a prescribed attenuation level the robust fuzzy h infty estimator based stabilization design problem can be formulated as a diffusion matrix inequality dmi problem to solve dmis via the traditional algebraic matrix techniques we utilize the divergence theorem and the poincare inequality to transform the dmis into bilinear matrix inequalities with a poincare constant defined according to the spatial domain of the corresponding pds finally the robust fuzzy h infty estimator based stabilization design problem can be effectively solved by a set of linear matrix inequalities instead of the bmis with the help of the proposed decoupled method additionally an optimal robust fuzzy h infty estimator based stabilization design can be realized via minimizing the noise attenuation level a simulation example is provided to illustrate the design procedure and verify the performance of the proposed optimal design

stability analysis of lattice boltzmann methods the lattice boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered although the equation is a derivative of lattice gas automata it may be interpreted as a lagrangian finite difference method for the numerical simulation of the discrete velocity boltzmann equation that makes use of a bgk collision operator as a result it is not surprising that numerical instability of lattice boltzmann methods have been frequently encountered by researchers we present an analysis of the stability of perturbations of the particle populations linearized about equilibrium values corresponding to a constant density uniform mean flow the linear stability depends on the following parameters the distribution of the mass at a site between the different discrete speeds the bgk relaxation time the mean velocity and the wavenumber of the perturbations this parameter space is too large to compute the complete stability characteristics we report some stability results for a subset of the parameter space for a 7 velocity hexagonal lattice a 9 velocity square lattice and a 15 velocity cubic lattice results common to all three lattices are 1 the bgk relaxation time must be greater than 12 corresponding to positive shear viscosity 2 there exists a maximum stable mean velocity for fixed values of the other parameters and 3 as is increased from 12 the maximum stable velocity increases monotonically until some fixed velocity is reached which does not change for larger

control synthesis for discrete time t s fuzzy systems based on membership function dependent h_ infty performance this article focuses on disturbance attenuation problem for discrete time takagi sugeno t s fuzzy systems first a membership function dependent h infty performance index is proposed by which different performance can be achieved for local subsystems then the better performance may be obtained for the t s fuzzy system that works on a particular local subsystem most of the time it may guarantee better control effects in practical engineering applications with the help of the newly defined performance index and fuzzy lyapunov functions an observer based feedback control scheme is presented in the form of linear matrix inequalities in simulation the performance index obtained by this article can be improved by about 10 than that obtained by the traditional h infty control method

finite volume lattice boltzmann schemes in two and three dimensions simple and practical finite volume schemes for the lattice boltzmann equation are derived in two and three dimensions through the application of modern finite volume methods the schemes use a finite volume vortextype formulation based on quadrilateral elements in two dimensions and trilinear hexahedral elements in three dimensions it is shown that the schemes are applicable to domains with irregular boundaries of arbitrary shape in two and three dimensions s1063 651x 99 10809 2

numerical stability of explicit off lattice boltzmann schemes the off lattice boltzmann olb method consists of numerical schemes which are used to solve the discrete boltzmann equation unlike the commonly used lattice boltzmann method the spatial and time steps are uncoupled in the olb method in the currently proposed schemes which can be broadly classified into runge kutta based and characteristics based the size of the time step is limited due to numerical stability constraints in this work we systematically compare the numerical stability of the proposed schemes in terms of the maximum stable time step in line with the overall lb method we investigate the available schemes where the advection approximation is explicit and the collision approximation is either explicit or implicit the comparison is done by implementing these schemes on benchmark incompressible flow problems such as taylor vortex flow poiseuille flow and lid driven cavity flow it is found that the characteristics based olb schemes are numerically more stable than the runge kutta based schemes additionally we have observed that with respect to time step size the scheme proposed by bardow et al 2006 1 is the most numerically stable and computationally efficient scheme compared to similar schemes for the flow problems tested here

lattice boltzmann simulations on irregular grids introduction of the natrium library the lattice boltzmann method is a modern approach to simulate fluid flow in its original formulation it is restricted to regular grids second order discretizations and a unity cfl number this paper describes our new off lattice boltzmann solver natrium an extensible and parallel c code to perform lattice boltzmann simulations on irregular grids natrium also allows high order spatial discretizations and non unity cfl numbers to be used we demonstrate how these features can efficiently decrease the number of grid points required in a simulation and thus reduce the computational time compared to the standard lattice boltzmann method we detail the implementation of a recently proposed semi lagrangian lattice boltzmann method and prove its efficiency in comparisons to other state of the art off lattice boltzmann schemes

acceleration of steady state lattice boltzmann simulations on non uniform mesh using local time step method in this paper the local time step method is applied to the lattice boltzmann method lbm on non uniform grid generalized form of interpolation supplemented lbm gilbm for steady flow simulations the local time step method is known to be an effective technique to accelerate the solution to the converged steady state on non uniform grid first code validation for global time step method is performed by solving flow around a cylinder at low reynolds numbers our results show good agreement with previous studies two dimensional flow simulations around an airfoil were performed in order to validate the code using the local time step method and the results are compared with the global time step solutions the pressure distribution and the aerodynamic coefficients of global and local time step results are in good agreement they are also consistent with the previous studies at the same time cpu time required to obtain the steady state solutions using the local time step are reduced by 70 80 compared with that using global time step

high order upwind compact finite difference lattice boltzmann method for viscous incompressible flows abstract in this work a high order upwind compact finite difference lattice boltzmann method ucdlbm is developed to efficiently solve viscous incompressible flow problems a fifth order upwind compact difference scheme is adopted to discretize the spatial derivatives of the lattice boltzmann equation and the third order total variation diminishing runge kutta scheme is utilized for the discretization of the temporal term compared to the existing central compact finite difference lattice boltzmann method cfdlbm the present ucdlbm can prevent non physical oscillations without filtering due to the natural dissipative property of upwind schemes three benchmark problems involving the taylor green vortex problem the doubly periodic shear layer flow problem and the lid driven square cavity flow problem are numerically solved to demonstrate the accuracy and efficiency of the present method numerical results computed are in good agreement with the analytical solution or other available numerical results and the present ucdlbm is less time consuming than the cfdlbm without degenerating the order of accuracy of the numerical solutions

polynomial fuzzy observed state feedback stabilization via homogeneous lyapunov methods a homogeneously state dependent polynomial lyapunov function for an observed state feedback polynomial fuzzy control system is proposed from which an advanced sufficient sum of squares sos condition formulated in terms of state dependent matrix inequalities to achieve fuzzy stabilization is derived three main features compared with existing nonhomogeneously polynomial methods are as follows 1 homogeneous lyapunov function and its time derivative are nicely linked via the hessian matrix 2 removing the nonconvex obstacles on dot p x when deriving a nonhomogeneous lyapunov stabilization condition dot v x 3 separation principle holds since common p falls out as a special case the proposed homogeneous sos approach is placed ahead of the existing sos based methods found in polynomial fuzzy stabilization controls to verify the problem solving theories of the homogeneous polynomial method announced four examples are demonstrated to show the promising features of the approach adduced finally an appendix illustrating the solving procedure is added for clarification on how the examples are solved via sos

a new splitting scheme to the discrete boltzmann equation for non ideal gases on non uniform meshes we present a novel numerical procedure for solving the discrete boltzmann equations dbe on non uniform meshes our scheme is based on the strang splitting method where we seek to investigate two phase flow applications in this note we investigate the onset of parasitic currents which arise in many computational two phase algorithms to the best of our knowledge the results presented in this work show for the first time a spectral element discontinuous galerkin sedg discretization of a discrete boltzmann equation which successfully eliminates parasitic currents on non uniform meshes with the hope that this technique can be used for applications in complex geometries calculations are performed on non uniform mesh distributions by using high order spectral body fitting quadrilateral elements validation and verification of our work is carried out by comparing results against the classical 2d younglaplace law problem for a static drop

implementation of a high order compact finite difference lattice boltzmann method in generalized curvilinear coordinates abstract in this work the implementation of a high order compact finite difference lattice boltzmann method cfdlbm is performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle curved geometries with non uniform grids the incompressible form of the discrete boltzmann equation with the bhatnagar gross krook bgk approximation with the pressure as the independent dynamic variable is transformed into the generalized curvilinear coordinates herein the spatial derivatives in the resulting lattice boltzmann lb equation in the computational plane are discretized by using the fourth order compact finite difference scheme and the temporal term is discretized with the fourth order runge kutta scheme to provide an accurate and efficient incompressible flow solver a high order spectral type low pass compact filter is used to regularize the numerical solution and remove spurious waves generated by boundary conditions flow non linearities and grid non uniformity all boundary conditions are implemented based on the solution of governing equations in the generalized curvilinear coordinates the accuracy and efficiency of the solution methodology presented are demonstrated by computing different benchmark steady and unsteady incompressible flow problems a sensitivity study is also conducted to evaluate the effects of grid size and filtering on the accuracy and convergence rate of the solution four test cases considered herein for validating the present computations and demonstrating the accuracy and robustness of the solution algorithm are unsteady couette flow and steady flow in a 2 d cavity with non uniform grid and steady and unsteady flows over a circular cylinder and the naca0012 hydrofoil at different flow conditions results obtained for the above test cases are in good agreement with the existing numerical and experimental results the study shows the present solution methodology based on the implementation of the high order compact finite difference lattice boltzmann method cfdlbm in the generalized curvilinear coordinates is robust efficient and accurate for solving steady and unsteady incompressible flows over practical geometries

quadratic stability analysis of the takagi sugeno fuzzy model the nonlinear dynamic takagi sugeno fuzzy model with offset terms is analyzed as a perturbed linear system a sufficient criterion for the robust stability of this nominal system against nonlinear perturbations guarantees quadratic stability of the fuzzy model the criterion accepts a convex programming formulation of reduced computational cost compared to the common lyapunov matrix approach parametric robust control techniques suggest synthesis tools for stabilization of the fuzzy system application examples on fuzzy models of nonlinear plants advocate the efficiency of the method the examples demonstrate reduced conservatism compared to norm based criteria

relaxed stabilization criterion for t s fuzzy systems by minimum type piecewise lyapunov function based switching fuzzy controller this paper proposes the minimum type piecewise lyapunov function based switching fuzzy controller that switches accompanying the piecewise lyapunov function by applying this switching fuzzy controller with the minimum type piecewise lyapunov function the relaxed stabilization criterion is obtained for continuous takagi sugeno t s fuzzy systems some conditions of the relaxed stabilization criterion are represented by bilinear matrix inequalities bmis which contain some bilinear terms as the product of a full matrix and a scalar according to the literature the path following method is very effective for this kind of bmi problem hence it is utilized to obtain solutions of the criterion xie et al in 1997 chose two types i e minimum type and maximum type of piecewise lyapunov functions as the lyapunov function candidates the reasons for why this study only chooses the minimum type piecewise lyapunov function as the lyapunov function candidate are illustrated moreover the numerical example shows the relaxation of the proposed criterion

a lattice boltzmann algorithm for calculation of the laminar jet diffusion flame a new two distribution lattice boltzmann equation lbe algorithm is presented to solve the laminar diffusion flames within the context of burke schumann flame sheet model one distribution models the transport of the schvab zeldovich coupling function or the mixture fraction to combine the energy and species equations the other distribution models the quasi incompressible navier stokes equations with the low mach number approximation in the quasi incompressible flows the thermodynamics quantities depend on the coupling function but not on the hydrodynamic pressure and the fluid components are assumed to be compressible only in the mixing reaction region a systematic and consistent approach to deriving lbes for the general advection diffusion equation and the quasi incompressible navier stokes equations are also presented the streaming step of the lbes are discretized by the total variation diminishing tvd lax wendroff scheme numerical simulations are carried out to reproduce the low frequency flame oscillation or flame flicker of buoyant jet diffusion flame comparison between the quasi incompressible model and the incompressible model is presented and the role of non solenoidal velocity is examined

on the finite difference based lattice boltzmann method in curvilinear coordinates the lattice boltzmann method is a microscopic based approach for solving the fluid flow problems at the macroscopic scales the presently popular method uses regularly spaced lattices and cannot handle curved boundaries with desirable flexibility to circumvent such difficulties a finite difference based lattice boltzmann method fdlbm in curvilinear coordinates is explored using body fitted coordinates with non uniform grids several test cases including the impulsively started cylindrical couette flow steady state cylindrical couette flow steady flow over flat plates and steady flow over a circular cylinder are used to examine various issues related to the fdlbm the effect of boundary conditions for the distribution functions on the solution the merits between second order central difference and upwind schemes for advection terms and the effect of the reynolds number are investigated favorable results are obtained using fdlbm in curvilinear coordinates indicating that the method is potentially capable of solving finite reynolds number flow problems in complex geometries

nonquadratic cal h _ infty stabilization conditions for observer based t s fuzzy control systems this paper investigates the nonquadratic output feedback stabilization problem for nonlinear systems in takagi sugeno s t s form to achieve improved performance in the cal h infty sense this paper provides two kinds of relaxation techniques one for the case where all premise variables are measurable and one for the case where the premise variables are immeasurable in particular the emphasis of the second technique is the use of estimated premise variables for nonquadratic lyapunov functions

a characteristic galerkin method for discrete boltzmann equation abstract the characteristic galerkin finite element method for the discrete boltzmann equation is presented to simulate fluid flows in complex geometries the inherent geometric flexibility of the finite element method permits the easy use of simple cartesian variables on unstructured meshes and the mesh clustering near large gradients the characteristic galerkin procedure with appropriate boundary condition results in accurate solutions with little numerical diffusion several test cases are conducted including unsteady couette flows lid driven cavity flows and steady flow past a circular cylinder on unstructured meshes the numerical results are in good agreement with previous analytical if applicable numerical and experimental results

improved bounds on the average length of longest common subsequences it has long been known lchvatal and sankoff 1975r that the average length of the longest common subsequence of two random strings of length n over an alphabet of size k is asymptotic to kn for some constant k depending on k the value of these constants remains unknown and a number of papers have proved upper and lower bounds on them we discuss techniques involving numerical calculations with recurrences on many variables for determining lower and upper bounds on these constants to our knowledge the previous best known lower and upper bounds for 2 were those of dancik and paterson approximately 0 773911 and 0 837623 ldancik 1994 dancik and paterson 1995r we improve these to 0 788071 and 0 826280 this upper bound is less than the 2 given by steele s old conjecture see steele l1997 page 3r that 2 e 2 1 s2 a 0 828427 as steele points out experimental evidence had already suggested that this conjectured value was too high finally we show that the upper bound technique described here could be used to produce for any k a sequence of upper bounds converging to k though the computation time grows very quickly as better bounds are guaranteed

three time integration methods for incompressible flows with discontinuous galerkin boltzmann method abstract this paper presents three time integration methods for incompressible flows with finite element method in solving the lattice bgk boltzmann equation the space discretization is performed using nodal discontinuous galerkin method which employs unstructured meshes with triangular elements and high order approximation degrees the time discretization is performed using three different kinds of time integration methods namely direct decoupling and splitting from the storage cost temporal accuracy numerical stability and time consumption we systematically compare three time integration methods then benchmark fluid flow simulations are performed to highlight efficient time integration methods numerical results are in good agreement with others or exact solutions

performance evaluation of the general characteristics based off lattice boltzmann scheme and dugks for low speed continuum flows the general characteristics based off lattice boltzmann scheme proposed by bardow et al 1 hereafter bardow s scheme and the discrete unified gas kinetic scheme dugks 2 are two methods that successfully overcome the time step restriction by the collision time which is commonly seen in many other kinetic schemes in this work we first perform a theoretical analysis of the two schemes in the finite volume framework by comparing their numerical flux evaluations it is found that the effect of collision term is considered in the evaluation of the cell interface distribution function in both schemes which explains why they can overcome the time step restriction and can give accurate results even as the time step is much larger than the collision time the difference between the two schemes lies in the treatment of the integral of the collision term when evaluating the cell interface distribution function in which bardow s scheme uses the rectangular rule while dugks uses the trapezoidal rule the performance of the two schemes i e accuracy stability and efficiency are then compared by simulating several two dimensional flows including the unsteady taylorgreen vortex flow the steady lid driven cavity flow and the laminar boundary layer problem it is observed that dugks can give more accurate results than bardow s scheme with a same mesh size furthermore the numerical stability of bardow s scheme decreases as the courantfriedrichslewy cfl number approaches to 1 while the stability of dugks is not affected by the cfl number apparently as long as cfl 1 it is also observed that dugks is twice as expensive as the bardow s scheme with the same mesh size

h control of uncertain fuzzy continuous time systems a new kind of dynamical fuzzy model is proposed to represent the continuous time complex system which includes both linguistic information and system uncertainties a new stability analysis and control system design approach is developed for this kind of dynamical fuzzy model since the fuzzy model considers the norm bounded disturbance the controller design problem becomes a h control problem a constructive algorithm is developed to obtain the h feedback control law finally an example is given to illustrate the application of the method

a nonlinearly preconditioned inexact newton algorithm for steady state lattice boltzmann equations most existing methods for calculating the steady state solution of the lattice boltzmann equations are based on pseudo time stepping which often requires a large number of time steps especially for high reynolds number problems to calculate the steady state solution directly without the time integration in this paper we propose and study a nonlinearly preconditioned inexact newton algorithm with a domain decomposition based linear solver for parallelization more precisely the proposed algorithmic framework involves an implicit second order discretization a two level inexact newton method and a nonlinear elimination preconditioner to accelerate the convergence of newton iteration a nonstandard pollution removing coarse space is introduced for the two level method numerical experiments are presented to demonstrate the robustness and efficiency of the algorithm especially for problems at a high reynolds number a comparison is also included to show the superiority of the proposed approach over o

robust stabilization of the takagi sugeno fuzzy model via bilinear matrix inequalities quadratic stability has enabled mainly via the linear matrix inequality framework the analysis and design of a nonlinear control system from the local matrices of the system s takagi sugeno t s fuzzy model it is well known however that there exist stable differential inclusions hence t s fuzzy models whose stability is unprovable by a globally quadratic lyapunov function at present literature in the broader area of stability analysis suggests piecewise quadratic stability as a means to avoid such conservatism this paper generalizes the idea and proposes a framework that supports less conservative sufficient conditions for the stability of the t s model by using piecewise quadratic generalized lyapunov functions the advocated approach results in the formulation of the controller synthesis which herein aims for robust stabilization as a problem of bilinear rather than linear matrix inequalities simulation studies which include an algorithm for solution of bilinear matrix inequalities demonstrate the proposed method

h _ infty fuzzy observer based control for a class of nonlinear distributed parameter systems with control constraints an hinfin fuzzy observer based control design is proposed for a class of nonlinear parabolic partial differential equation pde systems with control constraints for which the eigenspectrum of the spatial differential operator can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement in the proposed control scheme galerkin s method is initially applied to the pde system to derive a nonlinear ordinary differential equation ode system that accurately describes the dynamics of the dominant slow modes of the pde system the resulting nonlinear ode system is subsequently represented by the takagi sugeno t s fuzzy model then based on the t s fuzzy model a fuzzy observer based controller is developed to stabilize the nonlinear pde system and achieve an optimized hinfin disturbance attenuation performance for the finite dimensional slow system while control constraints are respected the outcome of the hinfin fuzzy observer based control problem is formulated as a bilinear matrix inequality bmi optimization problem a local optimization algorithm that treats the bmi as a double linear matrix inequality is presented to solve this bmi optimization problem finally the proposed design method is applied to the control of the temperature profile of a catalytic rod to illustrate its effectiveness

robust fuzzy control of nonlinear systems with parametric uncertainties addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties the takagi sugeno t s fuzzy model is adopted for fuzzy modeling of the nonlinear system two cases of the t s fuzzy system with parametric uncertainties both continuous time and discrete time cases are considered in both continuous time and discrete time cases sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability for the t s fuzzy system with parametric uncertainties the sufficient conditions are formulated in the format of linear matrix inequalities the t s fuzzy model of the chaotic lorenz system which has complex nonlinearity is developed as a test bed the effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic lorenz system

observer based robust h sub spl infin control for fuzzy systems using two step procedure this paper investigates both robust h sub spl infin analysis and synthesis problems involving observer based fuzzy control via linear matrix inequality methods for which efficient optimization techniques are available the observer and controller are capable of disturbance rejection in the presence of unknown but bounded disturbance we present results in a unified fashion applicable to both continuous and discrete time problems with or without uncertainty finally the validity and applicability of the approach are demonstrated by examples

analysis of the parametric models of passive scalar transport used in the lattice boltzmann method abstract the paper is devoted to the analysis of passive scalar transport models used in the lattice boltzmann method the case of the pure advection process without physical diffusion is considered the models proposed by other authors the modifications of these models and new high order finite difference schemes based on the extended runge kutta like formulae are analyzed the attention is focused on the stability analysis analysis of the fictitious numerical effects and on the investigation of the sensitivity of accuracy order to the parameter values the stability analysis is based on the von neumann method the influence of the parameter values on the stability is demonstrated stability conditions are obtained numerical dispersion and diffusion are analyzed test problems with discontinuous and smooth initial conditions are considered the sensitivity of the accuracy order on the parameter values is analyzed

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

a descriptor representation approach to observer based h control synthesis for discrete time fuzzy systems this work is concerned with the observer based h control synthesis problem of discrete time takagi sugeno t s fuzzy systems with external disturbances the objective is to find a new way to design the controller and observer guaranteeing a prescribed h performance of the fuzzy system by the descriptor representation approach two new conditions for observer based h control synthesis are proposed based on various lyapunov function candidates which are in the form of linear matrix inequalities lmis a numerical example will be given to show the efficiency of the proposed method

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

lattice boltzmann method on curvilinear coordinates system using an interpolation based strategy the lattice boltzmann method is extended to apply to general curvilinear coordinate systems as an example a cylindrical coordinate system is used to simulate two dimensional flow around a circular cylinder numerical simulations are carried out for impulsive initial conditions with reynolds numbers up to 104 the agreement of our results with previous computational and experimental results is satisfactory compared with previous lattice boltzmann simulations of the same problem our new approach greatly enhances the computational efficiency

an eulerian description of the streaming process in the lattice boltzmann equation this paper presents a novel strategy for solving discrete boltzmann equation dbe for simulation of fluid flows this strategy splits the solution procedure into streaming and collision steps as in the lattice boltzmann equation lbe method the streaming step can then be carried out by solving pure linear advection equations in an eulerian framework this offers two significant advantages over previous methods first the relationship between the relaxation parameter and the discretization of the collision term developed from the lbe method is directly applicable to the dbe method the resulting dbe collision step remains local and poses no constraint on time step second decoupling of the advection step from the collision step facilitates implicit discretization of the advection equation on arbitrary meshes an implicit unstructured dbe method is constructed based on this strategy and is evaluated using several test cases of flow over a backward facing step lid driven cavity flow and flow past a circular cylinder the speedup of convergence for some cases improves by a factor of about 20

simulation of cavity flow by the lattice boltzmann method a detailed analysis is presented to demonstrate the capabilities of the lattice boltzmann method thorough comparisons with other numerical solutions for the two dimensional driven cavity flow show that the lattice boltzmann method gives accurate results over a wide range of reynolds numbers studies of errors and convergence rates are carried out compressibility effects are quantified for different maximum velocities and parameter ranges are found for stable simulations the paper s objective is to stimulate further work using this relatively new approach for applied engineering problems in transport phenomena utilizing parallel computers

a hybrid wavelet based adaptive immersed boundary finite difference lattice boltzmann method for two dimensional fluid structure interaction abstract a second generation wavelet based adaptive finite difference lattice boltzmann method fd lbm is developed in this paper in this approach the adaptive wavelet collocation method awcm is firstly to the best of our knowledge incorporated into the fd lbm according to the grid refinement criterion based on the wavelet amplitudes of density distribution functions an adaptive sparse grid is generated by the omission and addition of collocation points on the sparse grid the finite differences are used to approximate the derivatives to eliminate the special treatments in using the fd based derivative approximation near boundaries the immersed boundary method ibm is also introduced into fd lbm by using the adaptive technique the adaptive code requires much less grid points as compared to the uniform mesh code as a consequence the computational efficiency can be improved to justify the proposed method a series of test cases including fixed boundary cases and moving boundary cases are invested a good agreement between the present results and the data in previous literatures is obtained which demonstrates the accuracy and effectiveness of the present awcm ib lbm

a spectral element discontinuous galerkin lattice boltzmann method for nearly incompressible flows we present a spectral element discontinuous galerkin lattice boltzmann method for solving nearly incompressible flows decoupling the collision step from the streaming step offers numerical stability at high reynolds numbers in the streaming step we employ high order spectral element discontinuous galerkin discretizations using a tensor product basis of one dimensional lagrange interpolation polynomials based on gauss lobatto legendre grids our scheme is cost effective with a fully diagonal mass matrix advancing time integration with the fourth order runge kutta method we present a consistent treatment for imposing boundary conditions with a numerical flux in the discontinuous galerkin approach we show convergence studies for couette flows and demonstrate two benchmark cases with lid driven cavity flows for re 400 5000 and flows around an impulsively started cylinder for re 550 9500 computational results are compared with those of other theoretical and computational work that used a multigrid method a vortex method and a spectral element model

comparing incomplete sequences via longest common subsequence abstract inspired by scaffold filling a recent approach for genome reconstruction from incomplete data we consider a variant of the well known longest common subsequence problem for the comparison of two sequences the new problem called longest filled common subsequence aims to compare a complete sequence with an incomplete one i e with some missing elements longest filled common subsequence lfcs given a complete sequence a an incomplete sequence b and a multiset m of symbols missing in b asks for a sequence b obtained by inserting the symbols of m into b so that b induces a common subsequence with a of maximum length we investigate the computational and approximation complexity of the problem and we show that it is np hard and apx hard when a contains at most two occurrences of each symbol and we give a polynomial time algorithm when the input sequences are over a constant size alphabet we give a 3 5 approximation algorithm for the longest filled common subsequence problem finally we present a fixed parameter algorithm for the problem when it is parameterized by the number of symbols inserted in b that match symbols of a

analysis and design of fuzzy control systems using dynamic fuzzy state space models a discrete time fuzzy control system which is composed of a dynamic fuzzy model and a fuzzy state feedback controller is proposed stability of the fuzzy control system is discussed and two sufficient conditions to guarantee the stability of the system are given in terms of uncertain linear system theory an algorithm is developed to check the stability condition the controller design method is divided into two procedures one is to get the state feedback matrix by linear system theory in every local rule map the other is to determine conditions of global stability by using a nonlinear analysis method two examples are used to show the design method

on the longest common parameterized subsequence the well known problem of the longest common subsequence lcs of two strings of lengths n and m respectively is o nm time solvable and is a classical distance measure for strings another well studied string comparison measure is that of parameterized matching where two equal length strings are a parameterized match if there exists a bijection on the alphabets such that one string matches the other under the bijection all works associated with parameterized pattern matching present polynomial time algorithms there have been several attempts to accommodate parameterized matching along with other distance measures as these turn out to be natural problems e g hamming distance and a bounded version of edit distance several algorithms have been proposed for these problems in this paper we consider the longest common parameterized subsequence problem which combines the lcs measure with parameterized matching we prove that the problem is np hard and then show a couple of approximation algorithms for the problem

online parameterized dictionary matching with one gap abstract we study the online parameterized dictionary matching with one gap problem pdmog which is the following preprocess a dictionary d of d patterns where each pattern contains a special gap symbol that can match any string so that given a text t arriving online a character at a time we can report all the patterns from d that parameterized match to suffixes of the text that has arrived so far before the next character arrives two equal length strings are a parameterized match if there exists a bijection on the alphabets such that one string matches the other under the bijection the gap symbols are associated with bounds determining the possible lengths of matching strings online dictionary matching with one gap dmog captures the difficulty in a bottleneck procedure for cyber security as many digital signatures of viruses manifest themselves as patterns with a single gap parameterized match captures possible encryption of the patterns we also define the strict pdmog problem in which subpatterns of the same dictionary pattern should be parameterized matched via the same bijection this captures situations where subpatterns of a dictionary pattern are encoded simultaneously we study this problem for special case called alphabet saturated dictionairy where every subpattern contains all characters of the dictionary alphabet we use the following parameters to describe our results d is the total size of the dictionary not including the gaps plsc is the longest parameterized suffix chain of subpatterns in d op is the number of parameterized patterns occurrences in t and are the minimum left and maximum right gap borders in the non uniformly bounded dictionary case g d is the degeneracy of the graph g d representing dictionary d this graph is classified as sparse or dense according the value of the g d and plsc parameters we obtain o d preprocessing time space and o g d plsc plsc max m o p query time per text character algorithm for online pdmog with sparse graph dictionaries o d d preprocessing time space and o plsc d plsc max m o p query time per text character algorithm for online pdmog with dense graph dictionaries o d preprocessing time space and o g d plsc o p query time per text character algorithm for strict pdmog with alphabet saturated dictionaries these results are parallel to the ones obtained for the dictionary with one gap dmog problem almost matching the lower bounds achieved for this problem 7 while the parameter g d can be as large as d and much lager if the dictionary has non uniform gap boundaries and the parameter plsc could theoretically be as large as d in many practical situations these parameters are actually small the strength of our work is in achieving results that explore and exploit small values for these parameters thus supplying algorithms that are suitable for some practical cyber security needs

robust fuzzy h control for uncertain nonlinear systems via state feedback an lmi approach this paper presents a method for designing robust fuzzy h controllers which stabilize nonlinear systems and guarantee an induced l2 norm bound constraint on disturbance attenuation for all admissible uncertainties takagi and sugeno fuzzy models with uncertainties are used as the model for the uncertain nonlinear systems fuzzy control systems utilize the concept of the so called parallel distributed compensation pdc using a single quadratic lyapunov function the stability with decay rate and disturbance attenuation for takagi and sugeno fuzzy model with parameter uncertainties are discussed a sufficient condition for the presence of the robust fuzzy h controllers is then presented in terms of linear matrix inequalities lmis finally design examples of robust fuzzy h controllers for uncertain nonlinear systems are presented

technical communique observer based h fuzzy control design for t s fuzzy systems with state delays this paper is concerned with the problem of observer based h fuzzy control design for takagi sugeno t s fuzzy systems with time delay the main contribution is that an effective matrix decoupling technique is developed to derive a single step lmi condition for observer based h control design this overcomes the drawback of two step lmi approach in the literature when restricted to delay free fuzzy systems the present result is shown less conservative than existing ones an illustrative example is given to show the effectiveness of our results