about simple fuzzy control and fuzzy control based on fuzzy relational equations abstract the paper discusses fuzzy controllers based on fuzzy relational equations in the case when fuzzy controllers inputs are exact godelian implication and minimum function as t norm are considered fuzzy relational equation with sup t composition results in plausible control and adjoint equation results in the simple fuzzy control min max inference method computation of fuzzy relations is not necessary relation between fuzzy plausible control and simple fuzzy control is discussed control algorithms are compared on simulation example

stability analysis of discrete time fuzzy model based control systems with time delay time delay independent approach this paper presents the stability analysis of discrete time fuzzy model based control systems with time delays to facilitate the stability analysis the t s fuzzy model is employed to represent the discrete time nonlinear system due to the multiplication property of the fuzzy model based control system the number of lmi based stability conditions is p p 1 2 where p is the number of rules for the fuzzy model and fuzzy controller consequently the computational demand for solving the solution to the stability conditions is very expensive especially when the value of p is large the problem becomes much worse when the relaxed stability conditions are formulated as huge matrices the huge matrices incorporate the information of all the closed loop subsystems which may cause the solution of the lmi based stability conditions difficult or even impossible to obtain owing to the limited computer power in this paper to reduce the computational demand the fuzzy model based control system is divided into parts which the control input will handle separately as a result the multiplication property of the fuzzy model based control system can be removed which effectively reduces the number of stability conditions to p and the computational demand for finding the solution can be reduced lmi based delay independent stability conditions are derived using the lyapunov based approach simulation examples are given to illustrate the effectiveness of the proposed approach

observer based fuzzy control for nonlinear networked systems under unmeasurable premise variables the problem of fuzzy observer based controller design is investigated for nonlinear networked control systems subject to imperfect communication links and parameter uncertainties the nonlinear networked control systems with parameter uncertainties are modeled through an interval type 2 it2 takagi sugeno t s model in which the uncertainties are handled via lower and upper membership functions the measurement loss occurs randomly both in the sensor to observer and the controller to actuator communication links specially a novel data compensation strategy is adopted in the controller to actuator channel the observer is designed under the unmeasurable premise variables case and then the controller is designed with the estimated states moreover the conditions for the existence of the controller can ensure that the resulting closed loop system is stochastically stable with the predefined disturbance attenuation performance two examples are provided to illustrate the effectiveness of the proposed method

on preconditioning the treecode accelerated boundary integral tabi poisson boltzmann solver abstract we recently developed a treecode accelerated boundary integral tabi solver for solving poisson boltzmann pb equation 1 the solver has combined advantages in accuracy efficiency memory and parallelization as it applies a well posed boundary integral formulation to circumvent many numerical difficulties associated with the pb equation and uses an o n log n treecode to accelerate the gmres iterative solver however as observed in our previous work 2 occasionally when the mesh generator produces low quality triangles the number of gmres iterations required to solve the discretized boundary integral equations a x b could be large to address this issue we design a preconditioning scheme using preconditioner matrix m such that m 1 a has much improved condition while m 1 z can be rapidly computed for any vector z in this scheme the matrix m carries the interactions between boundary elements on the same leaf only in the tree structure thus is block diagonal with many computational advantages the sizes of the blocks in m are conveniently controlled by the treecode parameter n 0 the maximum number of particles per leaf the numerical results show that this new preconditioning scheme improves the tabi solver with significantly reduced iteration numbers and better accuracy particularly for protein sets on which tabi solver previously converges slowly in addition this preconditioning scheme potentially can improve the condition number of various multipole method accelerated boundary elements solvers in scattering fluids elasticity etc

an implicit boundary integral method for computing electric potential of macromolecules in solvent abstract a numerical method using implicit surface representations is proposed to solve the linearized poisson boltzmann equation that arises in mathematical models for the electrostatics of molecules in solvent the proposed method uses an implicit boundary integral formulation to derive a linear system defined on cartesian nodes in a narrowband surrounding the closed surface that separates the molecule and the solvent the needed implicit surface is constructed from the given atomic description of the molecules by a sequence of standard level set algorithms a fast multipole method is applied to accelerate the solution of the linear system a few numerical studies involving some standard test cases are presented and compared to other existing results

robust stability analysis and systematic design of single input interval type 2 fuzzy logic controllers recent results on fuzzy control have shown that interval type 2 it2 fuzzy logic controllers flcs might achieve better control performance due to the additional degree of freedom provided by the footprint of uncertainty fou in their it2 fuzzy sets however the design and robust stability analysis of the it2 flcs are still challenging problems due to their relatively more complex internal structure in this paper we will derive the explicitly fuzzy mapping fm of a single input it2 flc sit2 flc to present design methods and investigate its robustness the analytical information of the it2 fm will give the opportunity to provide explanations on the roles of the fou parameters by taking advantage of the well developed framework of nonlinear control theory comparative theoretical explorations will be presented on the differences between the type 1 t1 fm and it2 fm to clearly show the role of the fou on the robust control system performance it will be proven that the robust stability of the it2 fuzzy system is guaranteed with the aids of the well known popov lyapunov method moreover analytical design methods are presented for sit2 flcs to generate commonly employed control curves by only tuning the size of the fous without a need of an optimization procedure it will be theoretically shown that the fou gives the opportunity to the sit2 flc to generate commonly employed nonlinear control curves while also providing a certain degree of robustness which cannot be accomplished by its t1 counterpart the presented results provide theoretical explanations on the role of the fou on the performance and robustness of the sit2 flc

chaos control of a fractional order modified coupled dynamos system abstract this paper analyzes some routh hurwitz stability conditions generalized to the fractional order case and discusses the stability region of the fractional order system we analyze the chaotic behavior of the fractional order modified coupled dynamos system concretely and provide the conditions suppressing chaos to unstable equilibrium points then use the feedback control method to control chaos in the fractional order modified coupled dynamos system numerical simulations show the effectiveness of the method

a two component matched interface and boundary mib regularization for charge singularity in implicit solvation abstract we present a new matched interface and boundary mib regularization method for treating charge singularity in solvated biomolecules whose electrostatics are described by the poisson boltzmann pb equation in a regularization method by decomposing the potential function into two or three components the singular component can be analytically represented by the green s function while other components possess a higher regularity our new regularization combines the efficiency of two component schemes with the accuracy of the three component schemes based on this regularization a new mib finite difference algorithm is developed for solving both linear and nonlinear pb equations where the nonlinearity is handled by using the inexact newton s method compared with the existing mib pb solver based on a three component regularization the present algorithm is simpler to implement by circumventing the work to solve a boundary value poisson equation inside the molecular interface and to compute related interface jump conditions numerically moreover the new mib algorithm becomes computationally less expensive while maintains the same second order accuracy this is numerically verified by calculating the electrostatic potential and solvation energy on the kirkwood sphere on which the analytical solutions are available and on a series of proteins with various sizes

interval type 2 fuzzy model predictive control of nonlinear networked control systems in this paper the problem of fuzzy predictive control of nonlinear networked control systems subject to parameter uncertainties and defective communication links is studied stochastic variables with bernoulli random binary distribution are used to represent the defective communication links with packets loss occurring intermittently between the controller and the physical plant an interval type 2 it2 takagi sugeno t s fuzzy model is employed to describe the nonlinear plant subject to parameter uncertainties which can be captured with the lower and upper membership functions the it2 fuzzy model and it2 fuzzy controller are not required to share the same lower and upper membership functions in order to design the state feedback fuzzy model predictive controller an optimization problem which minimizes the upper bound of a quadratic objective function subject to input constraints and packets dropout is formulated and solved at every sampling instant in the finite time horizon by introducing some slack matrices less conservative conditions are developed for system stability analysis two examples are given to demonstrate the effectiveness and merits of the proposed new design techniques

parametric adaptive control and parameter identification of low dimensional chaotic systems abstract the presented method of adaptive control corrects perturbations in the parameters of a system based on observations of its variables after a transient during which the desired parameter setting is reached exponentially quickly the system exhibits the goal behavior which can be a periodic quasiperiodic or chaotic solution of the equations of motion the length of the control transient scales inversely with the control strength and logarithmically with the magnitude of the original parameter perturbation it is shown that time series based models are capable of substituting for detailed knowledge of the system s nonlinear dynamics the method can be generalized to control more than one parameters to rely on observations of a single variable or to utilize a variety of control functions finally a method of parameter identification dual to the adaptive control is also discussed

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

asynchronous output feedback control of networked nonlinear systems with multiple packet dropouts t s fuzzy affine model based approach this paper investigates the problem of robust output feedback control for a class of networked nonlinear systems with multiple packet dropouts the nonlinear plant is represented by takagi sugeno t s fuzzy affine dynamic models with norm bounded uncertainties and stochastic variables that satisfy the bernoulli random binary distribution are adopted to characterize the data missing phenomenon the objective is to design an admissible output feedback controller that guarantees the stochastic stability of the resulting closed loop system with a prescribed disturbance attenuation level it is assumed that the plant premise variables which are often the state variables or their functions are not measurable so that the controller implementation with state space partition may not be synchronous with the state trajectories of the plant based on a piecewise quadratic lyapunov function combined with an s procedure and some matrix inequality convexifying techniques two different approaches to robust output feedback controller design are developed for the underlying t s fuzzy affine systems with unreliable communication links the solutions to the problem are formulated in the form of linear matrix inequalities lmis finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

a fast variational method for the construction of resolution adaptive c2 smooth molecular surfaces we present a variational approach to smooth molecular proteins nucleic acids surface constructions starting from atomic coordinates as available from the protein and nucleic acid data banks molecular dynamics md simulations traditionally used in understanding protein and nucleic acid folding processes are based on molecular force fields and require smooth models of these molecular surfaces to accelerate md simulations a popular methodology is to employ coarse grained molecular models which represent clusters of atoms with similar physical properties by psuedo atoms resulting in coarser resolution molecular surfaces we consider generation of these mixed resolution or adaptive molecular surfaces our approach starts from deriving a general form second order geometric partial differential equation in the level set formulation by minimizing a first order energy functional which additionally includes a regularization term to minimize the occurrence of chemically infeasible molecular surface pockets or tunnel like artifacts to achieve even higher computational efficiency a fast cubic b spline c 2 interpolation algorithm is also utilized a narrow band tri cubic b spline level set method is then used to provide c 2 smooth and resolution adaptive molecular surfaces

an efficient higher order fast multipole boundary element solution for poisson boltzmann based molecular electrostatics in order to compute polarization energy of biomolecules we describe a boundary element approach to solving the linearized poisson boltzmann equation our approach combines several important features including the derivative boundary formulation of the problem and a smooth approximation of the molecular surface based on the algebraic spline molecular surface state of the art software for numerical linear algebra and the kernel independent fast multipole method is used for both simplicity and efficiency of our implementation we perform a variety of computational experiments testing our method on a number of actual proteins involved in molecular docking and demonstrating the effectiveness of our solver for computing molecular polarization energy

a high order 3d boundary integral equation solver for elliptic pdes in smooth domains we present a high order boundary integral equation solver for 3d elliptic boundary value problems on domains with smooth boundaries we use nystrom s method for discretization and combine it with special quadrature rules for the singular kernels that appear in the boundary integrals the overall asymptotic complexity of our method is o n3 2 where n is the number of discretization points on the boundary of the domain and corresponds to linear complexity in the number of uniformly sampled evaluation points a kernel independent fast summation algorithm is used to accelerate the evaluation of the discretized integral operators we describe a high order accurate method for evaluating the solution at arbitrary points inside the domain including points close to the domain boundary we demonstrate how our solver combined with a regular grid spectral solver can be applied to problems with distributed sources we present numerical results for the stokes navier and poisson problems

noninteracting adaptive control of pmsm using interval type 2 fuzzy logic systems based on the type 2 fuzzy logic systems and adaptive control theory this paper develops a decentralized adaptive fuzzy controller for a permanent magnet synchronous motor pmsm the adaptive law is designed to compensate for the interconnection effects and the reconstruction errors using a sliding mode term the type 2 fuzzy logic systems are used to model the unknown functions based on lyapunov s stability theorem the stability of closed loop systems can be verified moreover the proposed overall control schemes guarantee that all the signals that are involved are bounded to demonstrate the effectiveness of the proposed methods simulation results are illustrated in this paper

the finite element approximation of the nonlinear poisson boltzmann equation a widely used electrostatics model in the biomolecular modeling community the nonlinear poisson boltzmann equation along with its finite element approximation are analyzed in this paper a regularized poisson boltzmann equation is introduced as an auxiliary problem making it possible to study the original nonlinear equation with delta distribution sources a priori error estimates for the finite element approximation are obtained for the regularized poisson boltzmann equation based on certain quasi uniform grids in two and three dimensions adaptive finite element approximation through local refinement driven by an a posteriori error estimate is shown to converge the poisson boltzmann equation does not appear to have been previously studied in detail theoretically and it is hoped that this paper will help provide molecular modelers with a better foundation for their analytical and computational work with the poisson boltzmann equation note that this article apparently gives the first rigorous convergence result for a numerical discretization technique for the nonlinear poisson boltzmann equation with delta distribution sources and it also introduces the first provably convergent adaptive method for the equation this last result is currently one of only a handful of existing convergence results of this type for nonlinear problems

synchronization of fractional order complex dynamical networks abstract in this letter the synchronization of complex dynamical networks with fractional order chaotic nodes is studied a fractional order controller for synchronization of complex network is presented some new sufficient synchronization criteria are proposed based on the lyapunov stability theory and the lasalle invariance principle these synchronization criteria can apply to an arbitrary fractional order complex network in which the coupling configuration matrix and the inner coupling matrix are not assumed to be symmetric or irreducible it means that this method is more general and effective numerical simulations of two fractional order complex networks demonstrate the universality and the effectiveness of the proposed method

quadrature over a pyramid or cube of integrands with a singularity at a vertex a simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex

numerical quadratures for layer potentials over curved domains in r 3 numerical quadratures for calculating simple and double layer potentials over curved domains in mathbb r 3 are given more generally these numerical quadratures are shown to be useful for evaluating surface integral involving kernels which are pseudohomogeneous of degree 1 in addition to potential flow problems such kernels are encountered when dealing with helmholtz problem stokes flow problems or linear elasticity problems

fuzzy model based fault tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults this paper addresses the problem of fault estimation and fault tolerant control for a class of takagi sugeno t s fuzzy ito stochastic systems subject to simultaneously sensor and actuator faults the main difficulty in this study is that sensor faults actuator faults and stochastic noise that are governed by brownian motion are taken into simultaneous consideration in a unified framework and traditional fault tolerant approaches are not effective to solve this research issue a new descriptor fuzzy sliding mode observer approach is presented in this paper to obtain the simultaneous estimates of system state sensor fault and actuator fault vectors based on the state estimates an observer based fault tolerant control ftc scheme is developed to stabilize the resulting closed loop system finally a simulation example is provided to show the effectiveness of the proposed fault tolerant approach

state and output feedback control of interval type 2 fuzzy systems with mismatched membership functions this paper is concerned with the problems of state and output feedback control for interval type 2 it2 fuzzy systems with mismatched membership functions the it2 fuzzy model and the it2 state and output feedback controllers do not share the same membership functions a novel performance index which is expressed as an extended dissipativity performance is introduced to be a generalization of h infty l 2 l infty passive and dissipativity performances indexes first the it2 takagi sugeno fuzzy model and the controllers are constructed by considering the mismatched membership functions second on the basis of lyapunov stability theory the it2 fuzzy state and output feedback controllers are designed respectively to guarantee that the closed loop system is asymptotically stable with extended dissipativity performance the existence conditions of the two kinds of controllers are obtained in terms of convex optimization problems which can be solved by standard software finally simulation results are provided to illustrate the effectiveness of the proposed methods

adaptive control of chaotic continuous time systems with delay a simple delay system governed by a first order differential delay equation may behave chaotically but the conditions for the system to have such behaviors have not been well recognized in this paper a set of rules is postulated first for the conditions for the delay system to display chaos a model reference adaptive control scheme is then proposed to control the chaotic system state to converge to an arbitrarily given reference trajectory with certain and uncertain system parameters numerical examples are given to analyze the chaotic behaviors of the delay system and to demonstrate the effectiveness of the proposed adaptive control scheme

heat conduction modeling by using fractional order derivatives the article deals with the heat conduction modeling a brief historical overview of the authors who have dealt with the heat conduction and overview of solving methods is listed in the introduction of article in the next section a mathematical model of one dimensional heat conduction with using derivatives of integer and fractional order is described the methods of solving models of heat conduction are described namely analytical and numerical methods in the case of numerical methods regards the finite difference method by using grunwald letnikov definition for the fractional time derivative implementation of these individual methods was realized in matlab the two libraries of m functions for the heat conduction model have been created namely heat conduction toolbox and fractional heat conduction toolbox at the conclusion of the article the simulations examples with using toolboxes are listed

event triggered fuzzy control for nonlinear networked control systems abstract this paper investigates the problem of event triggered et dynamic output feedback controller dofc design for nonlinear networked control systems ncss in the framework of interval type 2 it2 fuzzy systems the parameter uncertainties in the nonlinear plant can be captured effectively by utilizing the membership functions with upper and lower bounds to reduce the utilization of limited network bandwidth an et communication mechanism is applied a novel type of dofc subject to parameter uncertainties et communication mechanism and transmission delay is proposed where the membership functions are different from those of the fuzzy models consequently the closed loop system is with mismatched membership functions which hampers the stability analysis and controller design to promote the stability analysis and achieve a better control performance the information of membership functions and slack matrices are utilized for obtaining the main results finally a simulation example is employed to demonstrate the effectiveness of the proposed mechanism

experimental study of intelligent controllers under uncertainty using type 1 and type 2 fuzzy logic uncertainty is an inherent part in control systems used in real world applications the use of new methods for handling incomplete information is of fundamental importance type 1 fuzzy sets used in conventional fuzzy systems cannot fully handle the uncertainties present in control systems type 2 fuzzy sets that are used in type 2 fuzzy systems can handle such uncertainties in a better way because they provide us with more parameters and more design degrees of freedom this paper deals with the design of control systems using type 2 fuzzy logic for minimizing the effects of uncertainty produced by the instrumentation elements environmental noise etc the experimental results are divided in two classes in the first class simulations of a feedback control system for a non linear plant using type 1 and type 2 fuzzy logic controllers are presented a comparative analysis of the systems response in both cases was performed with and without the presence of uncertainty for the second class a non linear identification problem for time series prediction is presented based on the experimental results the conclusion is that the best results are obtained using type 2 fuzzy systems

an analysis of quadrature errors in second kind boundary integral methods this paper considers the effect of quadrature errors on galerkin methods for approximating the solution of second kind fredholm integral equations with weakly singular kernels defined on a smooth closed surface in three dimensions a quadrature strategy for galerkin methods that use piecewise poly nomials both continuous and discontinuous on a quadrilateral based mesh is proposed the error resulting from this further discretization is proved to be no larger than the original discretization error and moreover the amount of work needed to compute the resulting matrix for the corresponding linear system is shown to be proportional to the number of matrix entries

technical communique α dissipativity analysis of singular time delay systems in this paper the problem of delay dependent a dissipativity analysis is investigated for continuous time singular systems with time delay using the delay partitioning technique sufficient conditions are established in terms of linear matrix inequalities lmis which guarantees a singular system to be admissible and strictly q s r email protected in addition to delay dependence the obtained results are also dependent on the parameter a moreover the results of h performance analysis and passivity analysis are unified from the dissipative analysis results the results developed in this paper are less conservative than existing ones in the literature which are illustrated by several examples

a kernel independent adaptive fast multipole algorithm in two and three dimensions we present a new fast multipole method for particle simulations the main feature of our algorithm is that it does not require the implementation of multipole expansions of the underlying kernel and it is based only on kernel evaluations instead of using analytic expansions to represent the potential generated by sources inside a box of the hierarchical fmm tree we use a continuous distribution of an equivalent density on a surface enclosing the box to find this equivalent density we match its potential to the potential of the original sources at a surface in the far field by solving local dirichlet type boundary value problems the far field evaluations are sparsified with singular value decomposition in 2d or fast fourier transforms in 3d we have tested the new method on the single and double layer operators for the laplacian the modified laplacian the stokes the modified stokes the navier and the modified navier operators in two and three dimensions our numerical results indicate that our method compares very well with the best known implementations of the analytic fmm method for both the laplacian and modified laplacian kernels its advantage is the relative simplicity of the implementation and its immediate extension to more general kernels

a treecode accelerated boundary integral poisson boltzmann solver for electrostatics of solvated biomolecules abstract we present a treecode accelerated boundary integral tabi solver for electrostatics of solvated biomolecules described by the linear poisson boltzmann equation the method employs a well conditioned boundary integral formulation for the electrostatic potential and its normal derivative on the molecular surface the surface is triangulated and the integral equations are discretized by centroid collocation the linear system is solved by gmres iteration and the matrix vector product is carried out by a cartesian treecode which reduces the cost from o n 2 to o n log n where n is the number of faces in the triangulation the tabi solver is applied to compute the electrostatic solvation energy in two cases the kirkwood sphere and a solvated protein we present the error cpu time and memory usage and compare results for the poisson boltzmann and poisson equations we show that the treecode approximation error can be made smaller than the discretization error and we compare two versions of the treecode one with uniform clusters and one with non uniform clusters adapted to the molecular surface for the protein test case we compare tabi results with those obtained using the grid based apbs code and we also present parallel tabi simulations using up to eight processors we find that the tabi solver exhibits good serial and parallel performance combined with relatively simple implementation efficient memory usage and geometric adaptability

fast molecular solvation energetics and forces computation the total free energy of a molecule includes the classical molecular mechanical energy which is understood as the free energy in vacuum and the solvation energy which is caused by the change of the environment of the molecule solute from vacuum to solvent the solvation energy is important to the study of the intermolecular interactions in this paper we develop a fast surface based generalized born method to compute the electrostatic solvation energy along with the energy derivatives for the solvation forces the most time consuming computation is the evaluation of the surface integrals over an algebraic spline molecular surface asms and the fast computation is achieved by the use of the nonequispaced fast fourier transform nfft algorithm the main results of this paper involve a an efficient sampling of quadrature points over the molecular surface by using nonlinear patches b fast linear time estimation of energy and intermolecular forces c error analysis and d efficient implementation combining fast pairwise summation and the continuum integration using nonlinear patches

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

generating hyperchaotic lu attractor via state feedback control this paper constructs a new hyperchaotic system based on lu system by using a state feedback controller the detailed dynamical behaviors of this hyperchaotic system are further investigated including lyapunov exponents spectrum bifurcation and poincare mapping moreover a novel circuit diagram is designed for verifying the hyperchaotic behaviors and some experimental observations are also given