optimal control of non homogenous prey predator models during infinite and finite time intervals we propose a lattice to describe dynamics of two animal species population one being a prey and the other a predator the problem of controlling steady states of non homogenous prey predator model during finite and infinite time intervals is studied using lyapunov bellman technique the optimal control law is derived from the conditions that ensure the asymptotic stabilization of the steady states of this model using bellman s equation the densities of both prey and predator populations are obtained as functions of time graphical and numerical example studies of the obtained results are presented

exponential stabilization of nonholonomic chained systems this paper presents a feedback control scheme for the stabilization of two input driftless chained nonholonomic systems also called chained form these systems are controllable but not asymptotically stabilizable by a smooth static state feedback control law in addition exponential stability cannot be obtained with a smooth time varying feedback control law here global asymptotical stability with exponential convergence is achieved about any desired configuration by using a nonsmooth time varying feedback control law the control law depends in addition to the state and time on a function which is constant except at predefined instants of time where the function is recomputed as a nonsmooth function of the state the inputs are differentiable with respect to time and tend exponentially toward zero for use in the analysis a lemma on the exponential convergence of a stable time varying nonlinear system perturbed by an exponentially decaying signal is presented simulation results are also shown

robust finite time h control of singular stochastic systems via static output feedback abstract this paper addresses the problem of robust finite time stabilization of singular stochastic systems via static output feedback firstly sufficient conditions of singular stochastic finite time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time varying norm bounded disturbance then the results are extended to singular stochastic h finite time boundedness for the class of singular stochastic systems designed algorithm for static output feedback controller is provided to guarantee that the underlying closed loop singular stochastic system is singular stochastic h finite time boundedness in terms of strict linear matrix equalities with a fixed parameter finally an illustrative example is presented to show the validity of the developed methodology

variable structure exponential stabilization of chained systems based on the extended nonholonomic integrator abstract in this paper a new variable structure control strategy for exponentially stabilizing chained systems is presented based on the extended nonholonomic integrator model the discontinuous coordinate transformation and the reaching law method in variable structure control design the proposed approach converts the stabilization problem of an n dimensional chained system into the pole assignment problem of an n 3 dimensional linear time invariant system and consequently simplifies the stabilization controller design of nonholonomic chained systems

numerical investigation on the stability of singular driven cavity flow by applying the singularity subtraction technique to the unsteady driven cavity problem the stability of the impulsively started flow is investigated without smoothing the corner singularity a second order spectral projection method allows localization of the critical reynolds number for the first hopf bifurcation in the interval 8017 6 8018 8

accurate three dimensional lid driven cavity flow a chebyshev collocation method in space is introduced which allows an accurate calculation of three dimensional lid driven cavity flows the time integration is carried out by an adams bashforth backward euler scheme the accuracy of the method relies on the representation of the solution as a superposition of stationary local asymptotic solutions and a residual flow field this way the most severe discontinuities in the boundary conditions which arise along the lines where moving and stationary walls meet are taken care of analytically and thus do not spoil the numerical part of the solution calculations are carried out for no slip boundary conditions at the cavity end walls as well as for periodic end wall conditions in general the spatial accuracy is better than fifth order for rigid end wall conditions the accuracy is reduced near the end walls to o n 3 2 but recovers in the bulk tabulated data are provided for the most interesting flow properties

robust h sup spl infin filtering for uncertain markovian jump systems with mode dependent time delays this paper considers the problem of robust h sup spl infin filtering for uncertain markovian jump linear systems with time delays which are time varying and depend on the system mode the parameter uncertainties are time varying norm bounded the aim of this problem is to design a markovian jump linear filter that ensures robust exponential mean square stability of the filtering error system and a prescribed l sub 2 induced gain from the noise signals to the estimation error for all admissible uncertainties a sufficient condition for the solvability of this problem is obtained the desired filter can be constructed by solving a set of linear matrix inequalities an illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach

brief exponential stabilization of nonholonomic dynamic systems by smooth time varying control a general dynamic model is proposed for describing a large class of nonholonomic systems including extended chained systems extended power systems underactuated surface vessel systems etc by introducing an assistant state variable and a time varying state transformation based on the concept of minimal dilation degree this class of nonholonomic systems is transformed into linear time varying control systems and the asymptotic exponential stability is thus achieved by using a smooth time varying feedback control law the existence and uniqueness of the minimal dilation degree for the discussed systems are also proved under certain conditions

global finite time stabilisation for a class of stochastic high order time varying nonlinear systems abstractin this paper the problem of global finite time stabilisation by state feedback is investigated for a class of stochastic high order nonlinear systems with time varying nonlinearities based on the generalised stochastic lyapunov theorem on finite time stability and by skillfully using the method of adding a power integrator a continuous state feedback controller is successfully constructed to guarantee that the closed loop system is globally finite time stable in probability finally several simulation examples are provided to illustrate the effectiveness of the proposed method

h control for descriptor systems a matrix inequalities approach abstract this paper considers the h control problem for descriptor systems that possibly have impulsive modes and or j axis zeros first we propose matrix inequalities that give a generalized stability condition and an h norm condition for descriptor systems using these matrix inequalities we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed h norm condition as well as stabilizing the closed loop system and eliminating all impulsive modes these inequalities are equivalent to certain linear matrix inequalities to which we can get solutions whenever they exist using efficient polynomial time algorithms

technical communique finite time stability of linear time varying systems with jumps this paper deals with the finite time stability problem for continuous time linear time varying systems with finite jumps this class of systems arises in many practical applications and includes as particular cases impulsive systems and sampled data control systems the paper provides a necessary and sufficient condition for finite time stability requiring a test on the state transition matrix of the system under consideration and a sufficient condition involving two coupled differential difference linear matrix inequalities the sufficient condition turns out to be more efficient from the computational point of view some examples illustrate the effectiveness of the proposed approach

theory of stochastic dissipative systems by introducing the escape time a new definition of the dissipativity is introduced under some assumptions that are very reasonable for most physical models based on this definition criteria on the existence and the stability of the solution are presented which can be seen as the extension of lyapunov method to the non smooth case the dissipativity is applied to cascaded nonlinear stochastic systems and interconnected systems to display the superiority of the new framework which shows that there is no need to calculate the first exit time and the escape time

optimal motion planning for nonholonomic systems using genetic algorithm with wavelet approximation an optimal motion planning scheme using genetic algorithm with wavelet approximation is proposed for nonholonomic systems the motion planning of nonholonomic systems can be formulated as an optimal control of a driftfree system a cost function is introduced to incorporate the control energy and the final state errors the control inputs are determined to minimize the cost functional by using the method of wavelet the infinite dimensional optimal control problem is truncated to a finite dimensional one based on the wavelet bases the genetic algorithm is employed to solve a feasible trajectory satisfying nonholonomic constraints the proposed scheme is applied to a free floating robot consisting of two one link arms connected to a main base via revolute joints the numerical results demonstrate that the genetic algorithm with the wavelet approximation is an effective approach to steer a nonholonomic system from its initial state to its final state 2006 published by elsevier inc

homogeneous observers iterative design and global stabilization of high order nonlinear systems by smooth output feedback we study the problem of global stabilization by smooth output feedback for a class of n dimensional homogeneous systems whose jacobian linearization is neither controllable nor observable a new output feedback control scheme is proposed for the explicit design of both homogeneous observers and controllers while the smooth state feedback control law is constructed based on the tool of adding a power integrator the observer design is new and carried out by developing a machinery which makes it possible to assign the observer gains one by one in an iterative manner such design philosophy is fundamentally different from that of the traditional luenberger observer in which the observer gain is determined by observability in the case of linear systems our design method provides not only a new insight but also an alternative solution to the output feedback stabilization problem for a class of high order nonhomogeneous systems we further show how the proposed design method with an appropriate modification can still achieve global output feedback stabilization examples and simulations are given to demonstrate the main features and effectiveness of the proposed output feedback control schemes

fractional brownian motion and multifractional brownian motion of riemann liouville type the relationship between standard fractional brownian motion fbm and fbm based on the riemann liouville fractional integral or rl fbm is clarified the absence of stationary property in the increment process of rl fbm is compensated by a weaker property of local stationarity and the stationary property for the increments of the large time asymptotic rl fbm generalization of rl fbm to the rl multifractional brownian motion rl mbm can be carried out by replacing the constant holder exponent by a time dependent function rl mbm is shown to satisfy a weaker scaling property known as the local asymptotic self similarity this local scaling property can be translated into the small scale behaviour of the associated scalogram by using the wavelet transform

the kinematic laplacian equation method a novel procedure for the navier stokes equations in the vorticity velocity formulation is presented the time evolution of the vorticity is solved as an ode problem on each node of the spatial discretization using at each step of the time discretization the spatial solution for the velocity field provided by a new pde expression called the kinematic laplacian equation kle this complete decoupling of the two variables in a vorticity in time velocity in space split algorithm reduces the number of unknowns to solve in the time integration process and also favors the use of advanced ode algorithms enhancing the efficiency and robustness of time integration the issue of the imposition of vorticity boundary conditions is addressed as well as the details of the implementation of the kle by isoparametric finite element discretization we shall see some validation results of the kle method applied to the classical case of a circular cylinder in impulsive started pure translational steady motion at several reynolds numbers in the range 5

on robust stability of singular systems with random abrupt changes this paper deals with the class of continuous time singular linear systems with markovian switching sufficient conditions on stochastic stability and robust stochastic stability are developed in the lmi setting the developed sufficient conditions are used to check if either the nominal or the uncertain systems are regular impulse free and stochastically stable or robust stochastically stable

asymmetry in power law magnitude correlations time series of increments can be created in a number of different ways from a variety of physical phenomena for example in the phenomenon of volatility clustering well known in finance magnitudes of adjacent increments are correlated moreover in some time series magnitude correlations display asymmetry with respect to an increment s sign the magnitude of x i depends on the sign of the previous increment x i 1 here we define a model independent test to measure the statistical significance of any observed asymmetry we propose a simple stochastic process characterized by a an asymmetry parameter lambda and a method for estimating lambda we illustrate both the test and process by analyzing physiological data

robust reliable stabilization of stochastic switched nonlinear systems under asynchronous switching this paper is concerned with the problem of robust reliable control for a class of uncertain stochastic switched nonlinear systems under asynchronous switching where the switching instants of the controller experience delays with respect to those of the system a design scheme for the reliable controller is proposed to guarantee almost surely exponential stability for stochastic switched systems with actuator failures and the dwell time approach is utilized for the stability analysis then the approach is extended to take into account stochastic switched system with lipschitz nonlinearities and structured uncertainties finally a numerical example is employed to verify the proposed method

on the lyapunov theorem for singular systems in this paper we revisit the lyapunov theory for singular systems there are basically two well known generalized lyapunov equations used to characterize stability for singular systems we start with the lyapunov theorem of the work by lewis we show that the lyapunov equation of that theorem can lead to incorrect conclusion about stability some cases where that equation can be used are clarified we also show that an attempt to correct that theorem with a generalized lyapunov equation similar to the original one leads naturally to the generalized equation of takaba et al

fractionally integrated process with power law correlations in variables and magnitudes we propose a new stochastic process de ned by only two parameters 1 and 2 which generates power law correlations or anticorrelations in the variable increments and power law correlations in their magnitudes to account for empirical observations in a range of physical systems to demonstrate the utility of our process we consider the case with power law anticorrelations in the variable increments and power law correlations in their magnitudes to model scaling properties in heartbeat data the parameters 1 and 2 control separately the correlations in the increments and their magnitudes and we nd linear relations between each parameter and the corresponding correlation exponent

adaptive output feedback stabilization for nonholonomic systems with strong nonlinear drifts abstract this paper investigates the design of an output feedback adaptive stabilization controller for a nonholonomic chained system with strong nonlinear drifts including modeled nonlinear dynamics unmodeled dynamics and dynamics modeled with unknown parameters also the virtual control directions of the system are unknown the purpose is to design a nonlinear output feedback switching controller such that the closed loop system is globally asymptotically stable a novel observer and estimator are introduced for states and parameter estimates respectively a constructive procedure of design for an output feedback adaptive controller is given by using the integrator backstepping approach and based on the proposed observer and parameter estimator an example is given to show the effectiveness of the proposed scheme

spectral element methods for elliptic problems in nonsmooth domains engineering applications frequently require the numerical solution of elliptic boundary value problems in irregularly shaped domains for smooth problems spectral element methods have proved very successful since they can accommodate fairly complicated geometries while retaining a rapid rate of convergence geometric singularities however often give rise to singular solutions the accuracy of the spectral element methods is then degraded and they offer no apparent advantage over low order finite element methods in many cases however the singular structure of the solution is known and its form may be exploited by the spectral element method among the various ways of doing so through supplementary basis functions eigenfunction expansions and graded meshes the method of auxiliary mapping proves to be particularly effective for certain simple cases the problem is transformed to a coordinate system in which the solution is analytic and exponential convergence is recovered even when this is not possible the singularity is usually much weaker after mapping so that other treatments are more effective in the new coordinate system in this paper we study different ways of treating singularities and in particular the method of auxiliary mapping coupled with the use of supplementary basis functions error estimates are presented explaining why the combined approach is more effective and these estimates are confirmed through a number of numerical experiments for the laplace poisson and helmholtz equations

robust stability and stabilization of uncertain discrete time markovian jump linear systems this note deals with robust stability and control of uncertain discrete time linear systems with markovian jumping parameters systems with polytopic type parameter uncertainty in either the state space model matrices or in the transition probability matrix of the markov process are considered this note develops methods of robust stability analysis and robust stabilization in the mean square sense which are dependent on the system uncertainty the design of both mode dependent and mode independent control laws is addressed the proposed methods are given in terms of linear matrix inequalities numerical examples are provided to demonstrate the effectiveness of the derived results

technical communique new bounded real lemma for discrete time singular systems in this paper the problem of bounded real lemma for discrete time singular system with strict matrix inequalities is investigated it is proved that the bounded real lemma for discrete singular system can be described by a strict matrix inequality the results lead to more tractable and reliable computation when applying them to design control systems

finite time stability and stabilization of nonlinear stochastic hybrid systems this paper deals with the problem of finite time stability and stabilization of nonlinear markovian switching stochastic systems which exist impulses at the switching instants using multiple lyapunov function theory a sufficient condition is established for finite time stability of the underlying systems furthermore based on the state partition of continuous parts of systems a feedback controller is designed such that the corresponding impulsive stochastic closed loop systems are finite time stochastically stable a numerical example is presented to illustrate the effectiveness of the proposed method

nonholonomic motion planning steering using sinusoids methods for steering systems with nonholonomic c onstraints between arbitrary configurations are investigated suboptimal trajectories are derived for systems that are not in canonical form systems in which it takes more than one level of bracketing to achieve controllability are considered the trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level a class of systems that can be steered using sinusoids claimed systems is defined conditions under which a class of two input systems can be converted into this form are given

stabilization of nonholonomic chained systems via nonregular feedback linearization this paper addresses the problem of feedback stabilization of nonholonomic chained systems within the framework of nonregular feedback linearization firstly the nonsmooth version of nonregular feedback linearization is formulated and a criterion for nonregular feedback linearization is provided then it is proved that the chained form is linearizable via nonregular feedback control thus enable us to design feedback control laws using standard techniques for linear systems the obtained discontinuous control laws guarantee convergence of the closed loop system with exponential rates finally simulation results are presented to show the effectiveness of the approach

signal modeling with filtered discrete fractional noise processes filtered versions of fractionally differenced gaussian noise fdgn processes are studied fractionally differenced gaussian noise is a discrete time equivalent of fractional brownian motion filtered versions of such processes are ideally suited for modeling signals with different short term and long term correlation structure two iterative algorithms for estimating the parameters of filtered fdgn processes are described the first technique is based on the expectation maximization algorithm it converges to a stationary point of the log likelihood function corresponding to the parameters of the model the second technique is a computationally efficient approximate approach it is found to converge experimentally but no proof of its convergence is given the usefulness of filtered fdgn models and the performance of the proposed iterative algorithms are illustrated by fitting filtered fdgn models to speech waveforms and other data corresponding to natural phenomena

power law correlated processes with asymmetric distributions motivated by the fact that many physical systems display sid power law correlations together with siid an asymmetry in the probability distribution we propose a stochastic process that can model both properties the process depends on only two parameters where one controls the scaling exponent of the power law correlations and the other controls the degree of asymmetry in the distributions leaving the correlations unaffected we apply the process to air humidity data and find that the statistical properties of the process are in a good agreement with those observed in the data

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

technical communique finite time control of linear systems subject to parametric uncertainties and disturbances in this paper we consider finite time control problems for linear systems subject to time varying parametric uncertainties and to exogenous constant disturbances the main result provided is a sufficient condition for robust finite time stabilization via state feedback it can be applied to problems with both non zero initial conditions and unknown constant disturbances this condition is then reduced to a feasibility problem involving linear matrix inequalities lmis a detailed example is presented to illustrate the proposed methodology

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

a mixed basis spectral projection method a new grid less no collocation spectral projection method is presented the unsteady navier stokes equations are approximated according to the variational framework of guermond and quartapelle which accommodates two vector spaces for the velocity fields obtained in the two half steps of the fractional step method but retains only one in the final solution algorithm two different bases built on legendre polynomials are used for the velocity and pressure to solve the corresponding helmholtz and poisson equations by direct spectral elliptic solvers interpolations pn and pn 2 are employed for velocity and pressure to satisfy the lbb stability requirement and a gauss legendre quadrature formula with 3 2n integration points is used to prevent aliasing error in the pseudospectral evaluation of the nonlinear terms a bdf second order time stepping is implemented to provide accurate numerical results about the stability of the singular driven cavity problem

the stein james estimator for short and long memory gaussian processes summary we investigate the mean squared error of the stein james estimator for the mean when the observations are generated from a gaussian vector stationary process with dimension greater than two first assuming that the process is short memory we evaluate the mean squared error and compare it with that for the sample mean then a sufficient condition for the stein james estimator to improve upon the sample mean is given in terms of the spectral density matrix around the origin we repeat the analysis for gaussian vector long memory processes numerical examples clearly illuminate the stein james phenomenon for dependent samples the results have the potential to improve the usual trend estimator in time series regression models

a switching algorithm for global exponential stabilization of uncertain chained systems this note deals with chained form systems with strongly nonlinear unmodeled dynamics and external disturbances the objective is to design a robust nonlinear state feedback law such that the closed loop system is globally kexponentially stable we propose a novel switching control strategy involving the use of input state scaling and integrator backstepping the new features of our controllers include the ability to achieve lyapunov stability exponential convergence and robustness to a set of uncertain drift terms

control of high order nonholonomic systems in power chained form using discontinuous feedback addresses the problems of almost asymptotic stabilization and global asymptotic regulation gar for a class of high order nonholonomic systems in power chained form this particular class of nonlinear systems is an extension of a nonholonomic system in chained form that has received considerable attention in the past few years the nonholonomic system considered in this paper is not necessarily affine in the control variables and therefore cannot be handled by existing methods sufficient conditions are presented under which a discontinuous state feedback control law or a switching controller can be recursively constructed using the so called adding a power integrator technique of c qian et al 2001 we also illustrate how the results can be extend to multi input systems in power chained form simulation examples are provided to demonstrate the effectiveness of the proposed controllers

optimal control of an angular motion of a rigid body during infinite and finite time intervals this paper discusses the problem of optimal control of uniform angular motion of a rigid body containing an ideal fluid during both finite and infinite time intervals is studied by using lyapunov bellman technique using bellman equation the optimal control moments ensuring asymptotic stability of desired motion in both cases are obtained as non linear functions of the phase coordinates and time we are not concerned with the attitude of the body and consider only the evolution of the angular velocity as described by euler s equations the square of the euclidean norm of the perturbation of the angular velocity in both cases is estimated as a transcendental function of time

on lagrangian dynamics and its control formulations this paper exploits the equivalence between constrained dynamics problems and a class of tracking control problems an alternative derivation of the modern formulation of parczewski and blajer j appl math 56 1989 676 684 is presented including some new analysis on the almost singular case followed by a critique of the classical lagrangian formulation in addition a new formulation which allows the constraints to be satisfied approximately is presented a general closed loop control law which depends on a user specified threshold of constraint errors e is proposed transforming the default dae problem into a stiff ode initial value problem which can be routinely solved on computers it is shown that certain explosively unstable open loop systems may be stabilized by the use of closed loop control using a small but finite e an example is worked out using both the open loop and the closed loop control formulations

accurate ω ψ spectral solution of the singular driven cavity problem this article provides accurate spectral solutions of the driven cavity problem calculated in the vorticity stream function representation without smoothing the corner singularities a prima facie impossible task as in a recent benchmark spectral calculation by primitive variables of botella and peyret closed form contributions of the singular solution for both zero and finite reynolds numbers are subtracted from the unknown of the problem tackled here numerically in biharmonic form the method employed is based on a split approach to the vorticity and stream function equations a galerkin legendre approximation of the problem for the perturbation and an evaluation of the nonlinear terms by gauss legendre numerical integration results computed for re 0 100 and 1000 compare well with the benchmark steady solutions provided by the aforementioned collocation chebyshev projection method the validity of the proposed singularity subtraction scheme for computing time dependent solutions is also established

adaptive global stabilization of nonholonomic systems with strong nonlinear drifts a new input to state scaling scheme is first introduced to transform a class of nonholonomic systems in a chained form with strong nonlinear drifts and unknown constant parameters into a strict feedback form the backstepping technique is then applied to design a global adaptive stabilization controller a switching strategy based on the control input magnitude rather than the time is derived to get around the phenomenon of uncontrollability simulation examples validate the effectiveness of the proposed controller

output feedback adaptive stabilization control design for non holonomic systems with strong non linear drifts this paper investigates the problem of output feedback adaptive stabilization control design for non holonomic chained systems with strong non linear drifts including modelled non linear dynamics unmodelled dynamics and those modelled but with unknown parameters an observer and an estimator are introduced for state and parameter estimates respectively by using the integrator backstepping approach and based on the observer and parameter estimator a constructive design procedure for output feedback adaptive stabilization control is given it is shown that under some conditions the control design ensures the closed loop system is globally asymptotically stable when there is no non linear drift in the first subsystem and semiglobally asymptotically stable otherwise an example is given to show the effectiveness of the theory

global inverse optimal stabilization of stochastic nonholonomic systems abstract optimality has not been addressed in existing works on control of stochastic nonholonomic systems this paper presents a design of optimal controllers with respect to a meaningful cost function to globally asymptotically stabilize in probability nonholonomic systems affine in stochastic disturbances the design is based on the lyapunov direct method the backstepping technique and the inverse optimal control design a class of lyapunov functions which are not required to be as nonlinearly strong as quadratic or quartic is proposed for the control design thus these lyapunov functions can be applied to design of controllers for underactuated stochastic mechanical systems which are usually required lyapunov functions of a nonlinearly weak form the proposed control design is illustrated on a kinematic cart of which wheel velocities are perturbed by stochastic noise

discontinuous control of nonholonomic systems the problem of asymptotic convergence for a class of nonholonomic control systems via discontinuous control is addressed and solved from a new point of view it is shown that control laws which ensures asymptotic exponential convergence of the closed loop system can be easily designed if the system is described in proper coordinates in such coordinates the system is discontinuous hence the problem of local asymptotic stabilization for a class of discontinuous nonholonomic control systems is dealt with and a general procedure to transform a continuous system into a discontinuous one is presented moreover a general strategy to design discontinuous control laws yielding asymptotic convergence for a class of nonholonomic control systems is proposed the enclosed simulation results show the effectiveness of the method

robust stability and stabilization of a class of nonlinear discrete time stochastic systems an lmi approach abstract a problem of robust state feedback stability and stabilization of nonlinear discrete time stochastic processes is considered the linear rate vector of a discrete time system is perturbed by a nonlinear function that satisfies a quadratic constraint our objective is to show how linear constant feedback laws can be formulated to stabilize this type of nonlinear discrete time systems and at the same time maximize the bounds on this nonlinear perturbing function which the system can tolerate without becoming unstable the state dependent diffusion is modeled by a normal sequence of identically independently distributed random variables the new formulation provides a suitable setting for robust stabilization of nonlinear discrete time systems where the underlying deterministic systems satisfy the generalized matching conditions our method which is based on linear matrix inequalities lmis is distinctive from the existing robust control and absolute stability techniques examples are given to demonstrate the obtained results

adaptive control of nonlinearly parameterized systems the smooth feedback case studies global adaptive control of nonlinearly parameterized systems with uncontrollable linearization using a parameter separation technique and the tool of adding a power integrator we develop a feedback domination design approach for the explicit construction of a smooth adaptive controller that solves the problem of global state regulation in contrast to the existing results in the literature a key feature of our adaptive regulator is its minimum order property namely no matter how big the number of unknown parameters is the order of the dynamic compensator is identical to one and is therefore minimal as a consequence global state regulation of feedback linearizable systems with nonlinear parameterization is achieved by one dimensional adaptive controllers without imposing any extra e g convex concave conditions on the unknown parameters

galerkin spectral method for the vorticity and stream function equations a galerkin legendre spectral method for the solution of the vorticity and stream function equations in uncoupled form under no slip conditions in a square domain is presented which fully exploits the separation of variables in the two elliptic problems benefits from a nonsingular influence matrix and is able to solve the singular driven cavity problem modulo gibbs phenomenon even without regularizing the boundary condition at the corners

very high order compact finite difference schemes on non uniform grids for incompressible navier stokes equations this article presents a family of very high order non uniform grid compact finite difference schemes with spatial orders of accuracy ranging from 4th to 20th for the incompressible navier stokes equations the high order compact schemes on non uniform grids developed in shukla and zhong r k shukla x zhong derivation of high order compact finite difference schemes for non uniform grid using polynomial interpolation j comput phys 204 2005 404 for linear model equations are extended to the full navier stokes equations in the vorticity and streamfunction formulation two methods for the solution of helmholtz and poisson equations using high order compact schemes on non uniform grids are developed the schemes are constructed so that they maintain a high order of accuracy not only in the interior but also at the boundary second order semi implicit temporal discretization is achieved through an implicit backward differentiation scheme for the linear viscous terms and an explicit adam bashforth scheme for the non linear convective terms the boundary values of vorticity are determined using an influence matrix technique the resulting discretized system with boundary closures of the same high order as the interior is shown to be stable when applied to the two dimensional incompressible navier stokes equations provided enough grid points are clustered at the boundary the resolution characteristics of the high order compact finite difference schemes are illustrated through their application to the one dimensional linear wave equation and the two dimensional driven cavity flow comparisons with the benchmark solutions for the two dimensional driven cavity flow thermal convection in a square box and flow past an impulsively started cylinder show that the high order compact schemes are stable and produce extremely accurate results on a stretched grid with more points clustered at the boundary

control and stabilization of nonholonomic dynamic systems a class of inherently nonlinear control problems has been identified the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system models are presented for mechanical systems with nonholonomic constraints represented both by differential algebraic equations and by reduced state equations control issues for this class of systems are studied and a number of fundamental results are derived although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested

brief paper stability and stabilization of continuous time singular hybrid systems in this paper the problems of stability and state feedback stabilization for a class of continuous time singular hybrid systems are investigated a new sufficient and necessary condition for a continuous time singular hybrid system to be regular impulse free and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities lmis moreover a new sufficient and necessary condition is presented for the existence of the state feedback controller in terms of a set of coupled strict matrix inequalities finally a numerical example is given to illustrate the effectiveness of the obtained theoretical results

brief paper finite time control of discrete time linear systems analysis and design conditions in this paper we deal with some finite time control problems for discrete time time varying linear systems first we provide necessary and sufficient conditions for finite time stability these conditions require either the computation of the state transition matrix of the system or the solution of a certain difference lyapunov inequality then we address the design problem the proposed conditions allow us to find output feedback controllers which stabilize the closed loop system in the finite time sense all these conditions can be expressed in terms of lmis and therefore are numerically tractable as shown in the example included in the paper

exponential stabilization of driftless nonlinear control systems using homogeneous feedback this paper focuses on the problem of exponential stabilization of controllable driftless systems using time varying homogeneous feedback the analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control lie algebra it can be shown that any continuous time varying controller that achieves exponential stability relative to the euclidean norm is necessarily non lipschitz despite these restrictions we provide a set of constructive sufficient conditions for extending smooth asymptotic stabilizers to homogeneous exponential stabilizers the modified feedbacks are everywhere continuous smooth away from the origin and can be extended to a large class of systems with torque inputs the feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers

analysis of clusters formed by the moving average of a long range correlated time series we analyze the stochastic function c n i ensuremath equiv y i ensuremath y n i where y i is a long range correlated time series of length n mathrm max and y n i ensuremath equiv 1 n ensuremath sum k 0 n ensuremath 1 y i ensuremath k is the moving average with window n we argue that c n i generates a stationary sequence of self affine clusters mathcal c with length mathcal l lifetime ensuremath tau and area s the length and the area are related to the lifetime by the relationships mathcal l ensuremath sim ensuremath tau ensuremath psi mathcal l and s ensuremath sim ensuremath tau ensuremath psi s where ensuremath psi mathcal l 1 and ensuremath psi s 1 h we also find that mathcal l ensuremath tau and s are power law distributed with exponents depending on h p mathcal l ensuremath sim mathcal l ensuremath ensuremath alpha p ensuremath tau ensuremath sim ensuremath tau ensuremath ensuremath beta and p s ensuremath sim s ensuremath ensuremath gamma with ensuremath alpha ensuremath beta 2 ensuremath h and ensuremath gamma 2 1 h these predictions are tested by extensive simulations on series generated by the midpoint displacement algorithm of assigned hurst exponent h ranging from 0 05 to 0 95 of length up to n mathrm max 2 21 and n up to 2 13

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

stabilization of stochastic singular nonlinear hybrid systems abstract this paper deals with the control of the class of singular nonlinear stochastic hybrid systems under some appropriate assumptions results on stochastic stability and stochastic stabilization are developed two state feedback controllers linear and nonlinear that stochastically stabilize the class of systems we are considering are designed lmi sufficient conditions are developed to compute the gains of these controllers

efficient spectral galerkin method i direct solvers of second and fourth order equations using legendre polynomials this paper presents some efficient algorithms based on the legendre galerkin approximations for the direct solution of the second and fourth order elliptic equations the key to the efficiency of these algorithms is to construct appropriate base functions which lead to systems with sparse matrices for the discrete variational formulations the complexities of the algorithms are a small multiple of n d 1 operations for a d dimensional domain with n 1 d unknowns while the convergence rates of the algorithms are exponential for problems with smooth solutions in addition the algorithms can be effectively parallelized since the bottlenecks of the algorithms are matrix matrix multiplications

stability of linear stochastic systems via lyapunov exponents and applications to power systems this paper studies linear systems under sustained random perturbations the stochastic perturbation model is given by a bounded markov diffusion process as it appears e g in the description of load or generation uncertainties of power systems for such systems the lyapunov exponents describe necessary and sufficient conditions for almost sure asymptotic stability the paper presents several numerical methods for the computation of lyapunov exponents and applies this methodology to linear oscillators in dimension 2 and 3 and to a one machine infinite bus electric power system

adaptive repetitive control for a class of nonlinearly parametrized systems in this note lyapunov based adaptive repetitive control is presented for a class of nonlinearly parametrized systems through the use of an integral lyapunov function the controller singularity problem is elegantly solved as it avoids the nonlinear parametrization from entering into the adaptive control and repetitive control global stability of the adaptive system and asymptotic convergence of the tracking error are established and tracking error bounds are provided to quantify the control performance both partially and fully saturated learning laws are analyzed in detail and compared analytically

on bandlimitedness and lag limitedness of fractional gaussian noise abstract the contributions of this short paper are two fold we shall show two interesting properties of fractional gaussian noise fgn namely its bandlimitedness and lag limitedness the computation formulas for the maximum frequency of bandlimited fgn and the maximum lag of lag limited fgn are proposed in addition we will give a new explanation of the statistical dependences of fgn based on the present bandlimitedness and lag limitedness of fgn

adaptive stabilization of stochastic nonholonomic systems with nonlinear parameterization this paper investigates the problem of adaptive stabilization by state feedback for a class of stochastic nonholonomic systems in chained form with nonlinear parameterization a parameter separation technique is introduced to transform the nonlinear parameterized nonholonomic system into a linear like parameterized one then using input state scaling and backstepping techniques an adaptive state feedback controller is obtained based on switching strategy to eliminate the phenomenon of uncontrollability global asymptotic regulation in probability of the closed loop system states are guaranteed finally a simulation example is provided to illustrate the effectiveness of the proposed method

a transient higher order compact scheme for incompressible viscous flows on geometries beyond rectangular in this paper we propose an implicit high order compact hoc finite difference scheme for solving the two dimensional 2d unsteady navier stokes n s equations on irregular geometries on orthogonal grids our scheme is second order accurate in time and fourth order accurate in space it is used to solve three pertinent fluid flow problems namely the flow decayed by viscosity the lid driven square cavity and the flow in a constricted channel it is seen to efficiently capture both transient and steady state solutions of the n s equations with dirichlet as well as neumann boundary conditions apart from including the good features of hoc schemes our formulation has the added advantage of capturing transient viscous flows involving free and wall bounded shear layers which invariably contain spatial scale variations detailed comparison data produced by the scheme for all the three test cases are provided and compared with analytical as well as established numerical results excellent comparison is obtained in all the cases