predictive algorithms for neuromuscular control of human locomotion abstract the problem of quantifying muscular activity of the human body can be formulated as an optimal control problem the current methods used with large scale biomechanical systems are non derivative techniques these methods are costly as they require numerous integrations of the equations of motion additionally the convergence is slow making them impractical for use with large systems we apply an efficient numerical algorithm to the biomechanical optimal control problem using direct collocation with a trapezoidal discretization the equations of motion are converted into a set of algebraic constraint equations an augmented lagrangian formulation is used for the optimization problem to handle both equality and inequality constraints the resulting min max problem is solved with a generalized newton method in contrast to the prevalent optimal control implementations we calculate analytical first and second derivative information and obtain local quadratic convergence to demonstrate the efficacy of the method we solve a steady state pedaling problem with 7 segments and 18 independent muscle groups the computed muscle activations compare well with experimental emg data the computational effort is significantly reduced and solution times are a fraction of those of the non derivative techniques

switched nonlinear systems with state dependent dwell time the asymptotic convergence of a switched nonlinear system in the presence of disturbances is studied the system switches among a family of integral input to state stable systems the time between two consecutive switchings is not less than a value d this dwell time d is allowed to take different values according to a function whose argument is the state of the system at the switching times we propose a dwell time function which depends on the comparison functions which characterize the integral input to state stability property and guarantees the state of the switched system to converge to zero under the action of disturbances with bounded energy the main feature of the analysis is that it does not rely on the property for the switching to stop in finite time the two important cases of locally exponentially stable and feedforward systems are analyzed in detail

a small gain theorem for switched interconnected nonlinear systems and its applications a small gain theorem for switched interconnected nonlinear systems is set up which provides a tool for analyzing the behavior of switched systems also a method exploiting an average dwell time and the small gain technique is proposed based on the small gain theorem this technical note investigates the problem of global stabilization of switched nonlinear systems in strict feedback form whose all zero dynamics are input to state stable iss or only some are iss and others are not a sufficient condition for the global stabilization problem under a class of switching signals with average dwell time is derived by constructing state feedback controllers for subsystems the result is also applied to a class of switched nonlinear network control systems

delay independent minimum dwell time for exponential stability of uncertain switched delay systems in this technical note the problem of delay independent minimum dwell time for exponential stability of uncertain switched delay systems is considered piecewise time varying lyapunov functionals functions which are decreasing at switching times by construction are introduced to investigate exponential stability of switched delay systems with constant or time varying delays this type of delicately constructed lyapunov functionals functions can efficiently eliminate the jump phenomena of adjacent lyapunov functionals functions at switching times without imposing any restriction on the sizes of time delays by applying this type of lyapunov functionals functions it is shown that if each subsystem is delay independently exponentially stable then under some conditions there exists a delay independent minimum dwell time in the sense that the switched delay system with such minimum dwell time is exponentially stable irrespective of the sizes of the time delays two numerical examples are provided to demonstrate the efficiency of the proposed approach

input to state stabilization of switched nonlinear systems this note derives some sufficient conditions to ensure that the whole switched nonlinear system is input to state stabilizable iss when each mode is iss both cases that the switchings of system modes coincide exactly and that they do not coincide with those of the corresponding controllers are considered for the latter a model based identification scheme is used to identify the system modes the proposed scheme can overcome the finite escape time that may happen in this case

incomplete cholesky factorizations with limited memory we propose an incomplete cholesky factorization for the solution of large scale trust region subproblems and positive definite systems of linear equations this factorization depends on a parameter p that specifies the amount of additional memory in multiples of n the dimension of the problem that is available there is no need to specify a drop tolerance our numerical results show that the number of conjugate gradient iterations and the computing time are reduced dramatically for small values of p we also show that in contrast with drop tolerance strategies the new approach is more stable in terms of number of iterations and memory requirements

supervisory control of families of linear set point controllers 2 robustness a simply structured high level controller called a supervisor has recently been proposed in part i of this article ibid vol 41 1996 for the purpose of orchestrating the switching of a sequence of candidate set point controllers into feedback with an imprecisely modeled siso process so as to cause the output of the process to approach and track a constant reference input the process is assumed to be modeled by an siso linear system whose transfer function is in the union of a number of subclasses each subclass being small enough so that one of the candidate controllers would solve the set point tracking problem if the process transfer function was to be one of the subclass members this paper proves that without any further modification the same supervisor described in part i can also perform this function in the face of norm bounded unmodeled dynamics and moreover that none of the signals within the overall system can grow without bound in response to bounded disturbance and noise inputs whether they are constant or not

improved results on stability of continuous time switched positive linear systems in this paper the problems of stability for switched positive linear systems splss under arbitrary switching are investigated in a continuous time context the so called copositive polynomial lyapunov function cplf giving a generalization of copositive types of lyapunov function is first proposed which is formulated in a higher order form of the positive states of the underlying systems it is illustrated in this paper that some classical types of lyapunov functions can be seen as special cases of the proposed cplf then new stability conditions are developed by the new lyapunov function approach it is also proved that the conservativeness of the obtained criteria can be further reduced as the degree of the lyapunov function increases a numerical example is given to demonstrate the effectiveness and less conservativeness of the developed techniques

stability criteria of random nonlinear systems and their applications stochastic differential equations sdes are widely adopted to describe systems with stochastic disturbances while they are not necessarily the best models in some specific situations this paper considers the nonlinear systems described by random differential equations rdes the notions and the corresponding criteria of noise to state stability asymptotic gain and asymptotic stability are proposed in the m th moment or in probability several estimation methods of stochastic processes are presented to explain the reasonability of the assumptions used in theorems as applications of stability criteria some examples about stabilization regulation and tracking are considered respectively a theoretical framework on stability of rdes is finally constructed which is distinguished from the existing framework of sdes

modeling and adaptive tracking for a class of stochastic lagrangian control systems this paper focuses on the problem of modeling and adaptive tracking for a class of stochastic lagrangian control systems with unknown parameters by reasonably introducing random noise a method to construct stochastic lagrangian control systems is given under some milder assumptions an adaptive tracking controller is designed such that the mean square of the tracking error converges to an arbitrarily small neighborhood of zero by tuning design parameters the reasonability of assumptions and the efficiency of the controller are demonstrated by a mechanics model in random vibration environment

on signed incomplete cholesky factorization preconditioners for saddle point systems limited memory incomplete cholesky factorizations can provide robust preconditioners for sparse symmetric positive definite linear systems in this paper the focus is on extending the approach to sparse symmetric indefinite systems in saddle point form a limited memory signed incomplete cholesky factorization of the form ldl t is proposed where the diagonal matrix d has entries pm 1 the main advantage of this approach is its simplicity as it avoids the use of numerical pivoting instead a global shift strategy involving two shifts one for the 1 1 block and one for the 2 2 block of the saddle point matrix is used to prevent breakdown and to improve performance the matrix is optionally prescaled and preordered using a standard sparse matrix ordering scheme that is then postprocessed to give a constrained ordering that reduces the likelihood of breakdown and need for shifts the use of intermediate memory memory used in the construction of the incomplete factorization but subsequently d

a new pivoting strategy for gaussian elimination this paper discusses a method for determining a good pivoting sequence for gaussian elimination based on an algorithm for solving assignment problems the worst case complexity is o n3 in practice o n2 25 operations are sufficient

admissibility analysis of stochastic singular systems with poisson switching abstract this paper addresses the mean square admissibility problem for a class of stochastic singular systems with poisson switching by using h representation approach we show the equivalence between mean square admissibility and robust admissibility of a deterministic system which is an extension of the result in the case of deterministic system 1 based on multiple lyapunov functions and matrix decomposition approaches some easily verifiable sufficient conditions without equality constraint are established and can be conveniently used to state feedback controller design some admissibility criteria are constructed for linear singular systems with poisson switching three examples including a rlc circuit and a mass spring damper system are introduced to demonstrate the validity of the theoretical results

adaptive neural control for a class of switched nonlinear systems in this paper adaptive neural control is presented for a class of switched nonlinear systems with switching jumps and uncertainties in both system models and switching signals condition on limiting variation of the lyapunov function is given for input to state asymptotic stability of switched systems with switching jumps the control objective is achieved uniformly with respect to a class of switching signals the coupled difficulties from the discrepancy between control gains and switching jumps are overcome by discontinuous adaptive neural control combined with the classical adaptive control smooth approximations of the discontinuous controls are then presented for a systematic design procedure

stability of stochastic nonlinear systems with state dependent switching in this paper the problem of stability on stochastic systems with state dependent switching is investigated to analyze properties of the switched system by means of ito s formula and dynkin s formula it is critical to show switching instants being stopping times when the given active region set can be replaced by its interior the local solution of the switched system is constructed by defining a series of stopping times as switching instants and the criteria on global existence and stability of solution are presented by lyapunov approach for the case where the active region set can not be replaced by its interior the switched systems do not necessarily have solutions thereby quasi solution to the underlying problem is constructed and the boundedness criterion is proposed the significance of this paper is that all the results presented depend on some easily verified assumptions that are as elegant as those in the deterministic case and the proofs themselves provide design procedures for switching controls

stabilizing switching signals a transition from point wise to asymptotic conditions abstract characterization of classes of switching signals that ensure stability of switched systems occupies a significant portion of the switched systems literature this article collects a multitude of stabilizing switching signals under an umbrella framework we achieve this in two steps firstly given a family of systems possibly containing unstable dynamics we propose a new and general class of stabilizing switching signals secondly we demonstrate that prior results based on both point wise and asymptotic characterizations follow our result this is the first attempt in the switched systems literature where these switching signals are unified under one banner

invertibility of switched nonlinear systems this article addresses the invertibility problem for switched nonlinear systems affine in controls the problem is concerned with reconstructing the input and switching signal uniquely from given output and initial state we extend the concept of switch singular pairs introduced recently to nonlinear systems and develop a formula for checking if the given state and output form a switch singular pair a necessary and sufficient condition for the invertibility of switched nonlinear systems is given which requires the invertibility of individual subsystems and the nonexistence of switch singular pairs when all the subsystems are invertible we present an algorithm for finding switching signals and inputs that generate a given output in a finite interval when there is a finite number of such switching signals and inputs detailed examples are included to illustrate these newly developed concepts

brief paper input to state stability of switched systems and switching adaptive control in this paper we prove that a switched nonlinear system has several useful input to state stable iss type properties under average dwell time switching signals if each constituent dynamical system is iss this extends available results for switched linear systems we apply our result to stabilization of uncertain nonlinear systems via switching supervisory control and show that the plant states can be kept bounded in the presence of bounded disturbances when the candidate controllers provide iss properties with respect to the estimation errors detailed illustrative examples are included

output feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance abstract we address the class of stochastic output feedback nonlinear systems driven by noise whose covariance is time varying and bounded but the bound is not known a priori this problem is analogous to deterministic disturbance attenuation problems we first design a controller which guarantees that the solutions converge in probability to a residual set proportional to the unknown bound on the covariance then for the case of a vanishing noise vector field we design an adaptive controller which besides global stability in probability guarantees regulation of the state of the plant to zero with probability one

interval estimation for continuous time switched linear systems this paper deals with the design of interval observers for switched linear systems sls a class of hybrid systems under the assumption that the disturbances and the measurement noise are bounded upper and lower bounds for the state are calculated new conditions of cooperativity in discrete time instants are firstly proposed then some techniques for interval estimation are developed in continuous time it is shown that it is possible to calculate the observer gains making the estimation error dynamics cooperative and stable via some change of coordinates under arbitrary switching sequences the performances of the developed techniques are illustrated through numerical examples

input output to state stability and state norm estimators for switched nonlinear systems in this paper the concepts of input output to state stability ioss and state norm estimators are considered for switched nonlinear systems under average dwell time switching signals we show that when the average dwell time is large enough a switched system is ioss if all of its constituent subsystems are ioss moreover under the same conditions a non switched state norm estimator exists for the switched system furthermore if some of the constituent subsystems are not ioss we show that still ioss can be established for the switched system if the activation time of the non ioss subsystems is not too big again under the same conditions a state norm estimator exists for the switched system however in this case the state norm estimator is a switched system itself consisting of two subsystems we show that this state norm estimator can be constructed such that its switching times are independent of the switching times of the switched system it is designed for

exponential stability of stochastic systems with hysteresis switching for stochastic systems with state dependent switching which are motivated by active regions of subsystems the exponential stability is studied in this paper distinct from most of the existing references the existence of the solution to stochastic switched systems is not given as a priori information but can be proved under some easily verified conditions by the aid of dynkin s formula ito s formula and exponential martingale inequality the criteria on moment exponential stability and almost sure exponential stability of the stochastic switched system are established based on lyapunov like techniques simulation examples are presented to illustrate the validity of the results

analytic analysis of the force sharing among synergistic muscles in one and two degree of freedom models abstract mathematical optimization of specific cost functions has been used in theoretical models to calculate individual muscle forces measurements of individual muscle forces and force sharing among individual muscles show an intensity dependent non linear behavior it has been demonstrated that the force sharing between the cat gastrocnemius plantaris and soleus shows distinct loops that change orientation systematically depending on the intensity of the movement the purpose of this study was to prove whether or not static non linear optimization could inherently predict force sharing loops between agonistic muscles using joint moment data from a step cycle of cat locomotion the forces in three cat ankle plantar flexors gastrocnemius plantaris and soleus were calculated using two popular optimization algorithms and two musculo skeletal models the two musculo skeletal models included a one degree of freedom model that considered the ankle joint exclusively and a two degree of freedom model that included the ankle and the knee joint the main conclusion of this study was that solutions of the one degree of freedom model do not guarantee force sharing loops but the two degree of freedom model predicts force sharing loops independent of the specific values of the input parameters for the muscles and the musculo skeletal geometry the predicted force sharing loops were found to be a direct result of the loops formed by the knee and ankle moments in a moment moment graph

adaptive backstepping controller design using stochastic small gain theorem a more general class of stochastic nonlinear systems with unmodeled dynamics and uncertain nonlinear functions are considered in this paper with the concept of input to state practical stability isps and nonlinear small gain theorem being extended to stochastic case by combining stochastic small gain theorem with backstepping design technique an adaptive output feedback controller is proposed it is shown that the closed loop system is practically stable in probability a simulation example demonstrates the control scheme

switched adaptive control of switched nonlinearly parameterized systems with unstable subsystems this paper investigates the problem of adaptive stabilization for a class of switched nonlinearly parameterized systems where the solvability of the adaptive stabilization problem for subsystems is unnecessary a new switched adaptive control technique for the problem studied is set up by exploiting the generalized multiple lyapunov functions method and the parameter separation technique different update laws are designed to reduce the conservativeness caused by adoption of a common update law for all subsystems also the proposed technique permits removal of a common restriction in which the parameterization in the switched systems is restricted to a linear parameterization as an application of the proposed design technique stabilization for a class of non triangular switched systems with nonlinear parameterization is achieved by design of adaptive controllers since no subsystem of such a switched system is assumed to be adaptively stabilizable the problem under study cannot be handled by the existing methods a two inverted pendulums as a practical example is also provided to demonstrate the effectiveness of the proposed design method

preconditioning techniques for large linear systems a survey this article surveys preconditioning techniques for the iterative solution of large linear systems with a focus on algebraic methods suitable for general sparse matrices covered topics include progress in incomplete factorization methods sparse approximate inverses reorderings parallelization issues and block and multilevel extensions some of the challenges ahead are also discussed an extensive bibliography completes the paper

on lmi conditions to design observers for lipschitz nonlinear systems this paper addresses the problem of observer design for lipschitz nonlinear systems via lmi the goal of this note is to clarify some recent results and to propose a new design methodology this is based on the reformulation of the lipschitz property using some mathematical tools this reformulation is a relevant and useful lipschitz condition which leads to less restrictive lmi conditions to show the superiority of this latter two numerical examples are presented

on input to state stability of stochastic nonlinear systems with markovian jumping parameters in this article the input to state stability iss properties of stochastic nonlinear systems with markovian jump parameters are considered firstly the notions of stochastic iss e t weighted integral iss in mean and in the pth mean are introduced then by the lyapunov like function method some corresponding criteria are provided lastly a simulation example is provided to illustrate the effectiveness of our results

relaxed conditions for the input to state stability of switched nonlinear time varying systems this technical note considers the problem of input to state stability iss for switched nonlinear time varying systems first a sufficient condition is proposed to verify the iss of nonlinear time varying systems by using an improved lyapunov function then the results obtained are extended to study the iss of switched nonlinear time varying systems three relaxed conditions are given by using the methods of multiple lyapunov functions minimum dwell time and infinite switchings respectively comparing with the existing results the conditions obtained have two relaxations i e the derivative of lyapunov functions of subsystems are allowed to be indefinite and all subsystems are allowed to be unstable in the case of infinite switchings all results obtained also be used to study the uniformly asymptotic stability uas of systems finally a numerical example is given to illustrate the theoretical results

second order optimal control algorithm for complex systems the solution to large scale optimal control problems characterized by complex dynamics and extended time periods is often computationally demanding we present a solution algorithm with favourable local convergence properties as a way to reduce simulation times this method is based on using a trapezoidal direct collocation to convert the differential equations into algebraic constraints the resulting constrained minimization problem is then solved with an augmented lagrangian formulation to accommodate both equality and inequality constraints in contrast to the prevalent optimal control software implementations we calculate analytical first and second derivatives we then apply a generalized newton method to the augmented lagrangian formulation solving for all unknowns simultaneously the computational costs of the hessian formation and matrix solution remain manageable as the system size increases due to the sparsity of all tensor quantities likewise the total iterations for convergence scale well due to the local quadratic convergence of the generalized newton method we demonstrate the method with an inverted pendulum problem and a neuromuscular control problem with complex dynamics and 18 forcing functions the optimal control solutions are successfully found in both examples we obtain quadratic convergence rates in the neighbourhood of the solution copyright 2002 john wiley sons ltd

brief paper input to state stability and integral input to state stability of nonlinear impulsive systems with delays this paper is concerned with analyzing input to state stability iss and integral iss iiss for nonlinear impulsive systems with delays razumikhin type theorems are established which guarantee iss iiss for delayed impulsive systems with external input affecting both the continuous dynamics and the discrete dynamics it is shown that when the delayed continuous dynamics are iss iiss but the discrete dynamics governing the impulses are not the iss iiss property of the impulsive system can be retained if the length of the impulsive interval is large enough conversely when the delayed continuous dynamics are not iss iiss but the discrete dynamics governing the impulses are the impulsive system can achieve iss iiss if the sum of the length of the impulsive interval and the time delay is small enough in particular when one of the delayed continuous dynamics and the discrete dynamics are iss iiss and the others are stable for the zero input the impulsive system can keep iss iiss no matter how often the impulses occur our proposed results are evaluated using two illustrative examples to show their effectiveness

stability analysis of random nonlinear systems with time varying delay and its application this paper studies a class of random nonlinear systems with time varying delay in which the r order moment of the random disturbance is finite firstly some general conditions are proposed to guarantee the existence and uniqueness of the global solution to random nonlinear time delay systems secondly some criteria on noise to state stability in the moment sense and in probability sense are given by lyapunov method respectively finally an adaptive output feedback regulation controller is constructed for a class of random nonlinear time delay systems and the effectiveness of the proposed recursive procedure is demonstrated by a simulation example

output to state stability and detectability of nonlinear systems the notion of input to state stability iss has proved to be useful in nonlinear systems analysis this paper discusses a dual notion output to state stability oss a characterization is provided in terms of a dissipation inequality involving storage lyapunov functions combining iss and oss there results the notion of input output to state stability ioss which is also studied and related to the notion of detectability the existence of observers and output injection

a class of globally convergent optimization methods based on conservative convex separable approximations this paper deals with a certain class of optimization methods based on conservative convex separable approximations ccsa for solving inequality constrained nonlinear programming problems each generated iteration point is a feasible solution with lower objective value than the previous one and it is proved that the sequence of iteration points converges toward the set of karush kuhn tucker points a major advantage of ccsa methods is that they can be applied to problems with a very large number of variables say 104 105 even if the hessian matrices of the objective and constraint functions are dense

backstepping control in vector form for stochastic hamiltonian systems in this paper the problem of adaptive tracking for a class of stochastic hamiltonian control systems with unknown drift and diffusion functions is considered some difficulties come forth the integral chain consists of vectors and control and tracking errors are in different channels which are rarely considered in the existing references about stochastic nonlinear controls to resolve these problems an adaptive backstepping controller in vector form is designed such that the closed loop system has a unique solution that is globally bounded in probability and the fourth moment of the tracking error converges to an arbitrarily small neighborhood of zero as an application the modeling and the control for spring pendulum in stochastic surroundings are researched

temporal finite element formulation of optimal control in mechanisms a temporal finite element discretization of a boundary value problem has several advantages compared to a time integrating evolution form for optimized target movement simulations the paper gives some basic aspects on how such a finite element form can be stated with both displacements and controls discretized and seen as unknowns aspects on the resulting formulations are discussed important issues are the order continuity and fineness of the discretizations when the formulation is seen in an optimization context minimizing the effort for a prescribed movement the discretization affects the results obtained in several manners where some aspects of results are artifacts the paper discusses these effects from basic principles but also verifies them in numerical simulations

stochastic input to state stability and applications to global feedback stabilization notions of stochastic input to state stability are introduced and their lyapunov characterizations are established these notions constitute extensions of the deterministic iss proposed by e sonta

input to state stability of impulsive and switching hybrid systems with time delay this paper investigates input to state stability iss and integral input to state stability iiss of impulsive and switching hybrid systems with time delay using the method of multiple lyapunov krasovskii functionals it is shown that even if all the subsystems governing the continuous dynamics in the absence of impulses are not iss iiss impulses can successfully stabilize the system in the iss iiss sense provided that there are no overly long intervals between impulses i e the impulsive and switching signal satisfies a dwell time upper bound condition moreover these impulsive iss iiss stabilization results can be applied to systems with arbitrarily large time delays conversely in the case when all the subsystems governing the continuous dynamics are iss iiss in the absence of impulses the iss iiss properties can be retained if the impulses and switching do not occur too frequently i e the impulsive and switching signal satisfies a dwell time lower bound condition several illustrative examples are presented with their numerical simulations to demonstrate the main results

uniform input to state stability for switched and time varying impulsive systems we provide a lyapunov function based method for establishing different types of uniform input to state stability iss for time varying impulsive systems the method generalizes to impulsive systems with inputs the well established philosophy of assessing the stability of a system by reducing the problem to that of the stability of a scalar system given by the evolution of the lyapunov function on the system trajectories this reduction is performed in such a way that the resulting scalar system has no inputs novel sufficient conditions for iss are provided which generalize existing results for time invariant and time varying switched and nonswitched impulsive and nonimpulsive systems in several directions

output tracking control of nonlinear switched cascade systems using a variable structure control method this article is concerned with the output tracking control problem for a class of nonlinear switched cascade systems under some average dwell time based switching laws firstly stabilisation problem of this class of switched systems is considered then the result is extended to the output tracking control problem based on the variable structure control technique and the characteristic of the system the variable structure controllers and the average dwell time are designed the effectiveness of the proposed design approach is illustrated with simulation results

multiple lyapunov functions based small gain theorems for switched interconnected nonlinear systems multiple lyapunov functions mlfs based small gain theorems are presented for switched interconnected nonlinear systems with unstable subsystems which extend the small gain technique from its original non switched nonlinear version to a switched nonlinear version each low dimensional subsystem does not necessarily have the input to state stability iss property in the whole state space and it only has individual iss property in some subregions of the state space the novelty of this paper is that integral type mlfs and small gain techniques are utilized to establish some mlfs based small gain theorems for switched interconnected nonlinear systems which derive various stability results under some novel switching laws designed and construct integral type mlfs the small gain theorems proposed cover several recent results as special cases which also permit removal of a common restriction in which all low dimensional subsystems in switched interconnected systems are iss or only some are iss and others are not finally two illustrative examples are presented to demonstrate the effectiveness of the results provided

input to state stability and interconnections of discontinuous dynamical systems in this paper we will extend the input to state stability iss framework to continuous time discontinuous dynamical systems dds adopting piecewise smooth iss lyapunov functions the main motivation for investigating piecewise smooth iss lyapunov functions is the success of piecewise smooth lyapunov functions in the stability analysis of hybrid systems this paper proposes an extension of the well known filippov s solution concept that is appropriate for open systems so as to allow interconnections of dds it is proven that the existence of a piecewise smooth iss lyapunov function for a dds implies iss in addition a small gain iss interconnection theorem is derived for two dds that both admit a piecewise smooth iss lyapunov function this result is constructive in the sense that an explicit iss lyapunov function for the interconnected system is given it is shown how these results can be applied to construct piecewise quadratic iss lyapunov functions for piecewise linear systems including sliding motions via linear matrix inequalities

class kl estimates and input to state stability analysis of impulsive switched systems abstract in this paper we investigate input to state stability of impulsive switched systems the goal is to bridge two apparently different but both useful stability notions input to state stability and stability in terms of two measures in the hybrid systems setting based on two class kl function estimates and a comparison theorem for impulsive differential equations two sets of sufficient lyapunov type conditions for input to state stability in terms of two measures are obtained for impulsive switched systems these conditions exploit some nonlinear integral constraints in terms of generalized dwell time conditions to balance the continuous dynamics and impulsive dynamics so that input to state stability is achieved despite possible instability of individual continuous subsystems or destabilizing impulsive effects an illustrative example is presented together with numerical simulations to demonstrate the main results

robust adaptive fuzzy control of a class of uncertain switched nonlinear systems with mismatched uncertainties this paper studies the adaptive fuzzy control problem for a class of uncertain switched nonlinear systems with mismatched uncerta inties and external disturbances a new switched adaptive control technique for the problem studied is set up such that the considered switched systems can be stabilized under a class of switching signals characterized by the generalized average dwell time condition first the adaptive state feedback controller is designed based on tuning the estimations of the bounds on switching parameters instead of estimating the switching parameters directly next by using a switched observer to reconstruct the states of the system an output feedback controller is also presented in the design procedure fuzzy logic systems are used to approximate the unknown nonlinear functions to overcome the undesirable chattering phenomenon both control laws are developed using the continuous control strategy it is shown that both controllers can guarantee that all the signals in the resulting closed loop system are bounded finally two simulation examples are presented to demonstrate the effectiveness of the proposed control results

certainty equivalence implies detectability abstract it is shown that any stabilizing certainty equivalence control used within an adaptive control system causes the familiar interconnection of a controlled process and associated output estimator to be detectable through the estimator s output error e p for every frozen value of the index or parameter vector p upon which both the estimator and controller dynamics depend the fact that certainty equivalence implies detectability has been known for some time this has been shown to be so whenever the process model is linear and the controller and estimator models are also linear for every frozen value of p in this paper use is made of recently introduced concepts of input to state stability and detectability for nonlinear systems to prove that the same implication is valid in a more general nonlinear setting

input to state stability of impulsive stochastic delayed systems under linear assumptions in this paper the input to state stability iss integral iss iiss and stochastic iss siss are investigated for impulsive stochastic delayed systems by means of the lyapunov krasovskii function and the average impulsive interval approach the conditions for iss type properties are derived under linear assumptions respectively for destabilizing and stabilizing impulses it is shown that if the continuous stochastic delayed system is iss and the impulsive effects are destabilizing then the hybrid system is iss with respect to a lower bound of the average impulsive interval moreover it is unveiled that if the continuous stochastic delayed system is not iss the impulsive effects can successfully stabilize the system for a given upper bound of the average impulsive interval an improved comparison principle is developed for impulsive stochastic delayed systems which facilitates the derivations of our results for iss iiss siss an example of networked control systems is provided to illustrate the effectiveness of the proposed results

a new preconditioning technique for solving large sparse linear systems abstract a new sparse approximate triangular factorization technique for solving large sparse linear system by iterative methods is proposed the method is based on the description of the triangular factorization of a matrix as a product of elementary matrices and provides a general scheme for constructing incomplete preconditioners for the given matrix in particular the familiar incomplete choleski decomposition can be incorporated into this scheme the algorithm based on choice by value compares favorably with the incomplete choleski preconditioner and equipped with a user controlled parameter is able to tackle extremely ill conditioned problems arising in structural analysis semiconductor simulation oil reservoir modelling and other applications when applied to a positive definite symmetric matrix the algorithm produces a preconditioning matrix preserving that property

brief hysteresis based switching algorithms for supervisory control of uncertain systems we address the problem of controlling a linear system with unknown parameters ranging over a continuum by means of switching among a finite family of candidate controllers we present a new hysteresis based switching logic designed specifically for this purpose and derive a bound on the number of switches produced by this logic on an arbitrary time interval the resulting switching control algorithm is shown to provide stability and robustness to arbitrary bounded noise and disturbances and sufficiently small unmodeled dynamics

stochastic input to state stability of switched stochastic nonlinear systems in this paper global asymptotic stability in probability gasip and stochastic input to state stability siss for nonswitched stochastic nonlinear nssnl systems and switched stochastic nonlinear ssnl systems are investigated for the study of gasip the definition which we considered is not the usual notion of asymptotic stability in probability stability in probability plus attractivity in probability it can depict the properties of the system quantitatively correspondingly based on this definition some sufficient conditions are provided for nssnl systems and ssnl systems furthermore the definition of siss is introduced and corresponding criteria are provided for nssnl systems and ssnl systems in the proof of the above results to overcome the difficulties coming with the appearance of switching and the stochastic property at the same time we generalize the past comparison principle and fully use the properties of the functions which we constructed in terms of the average dwell time of the switching laws a sufficient siss condition is obtained for ssnl systems finally some examples are provided to demonstrate the applicability of our results

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

universal construction of feedback laws achieving iss and integral iss disturbance attenuation we study nonlinear systems with both control and disturbance inputs the main problem addressed in the paper is design of state feedback control laws that render the closed loop system integral input to state stable iiss with respect to the disturbances we introduce an appropriate concept of control lyapunov function iiss clf whose existence leads to an explicit construction of such a control law the same method applies to the problem of input to state stabilization converse results and techniques for generating iiss clfs are also discussed

absolute exponential stability and stabilization of switched nonlinear systems abstract this paper is concerned with the problems of absolute exponential stability and stabilization for a class of switched nonlinear systems whose system matrices are metzler nonlinearity of the systems is constrained in a sector field which is bounded by two odd symmetric piecewise linear functions multiple lyapunov functions are introduced to deal with the stability of such nonlinear systems compared with some existing results obtained by the common lyapunov function approach in the literature the conservatism of our results is reduced all present conditions can be solved by linear programming furthermore the absolute exponential stabilization for the considered systems is designed by the state feedback and average dwell time switching strategy two examples are also given to illustrate the validity of the theoretical findings

noise to state stability of random switched systems and its applications noise to state stability of random switched systems is investigated in this technical note by the aid of fubini s formula the criteria on noise to state stability in the moment of random switched systems are established under a reasonable assumption of second order processes as applications the control problems of spring pendulum in random environment are researched in addition nonlinear filtering is considered to ensure noise to state stability of filter error switched systems

multiple model self tuning control for a class of nonlinear systems this study develops a novel nonlinear multiple model self tuning control method for a class of nonlinear discrete time systems an increment system model and a modified robust adaptive law are proposed to expand the application range thus eliminating the assumption that either the nonlinear term of the nonlinear system or its differential term is global bounded the nonlinear self tuning control method can address the situation wherein the nonlinear system is not subject to a globally uniformly asymptotically stable zero dynamics by incorporating the pole placement scheme a novel nonlinear control structure based on this scheme is presented to improve control precision stability and convergence can be confirmed when the proposed multiple model self tuning control method is applied furthermore simulation results demonstrate the effectiveness of the proposed method

the method of moving asymptotes a new method for structural optimization a new method for non linear programming in general and structural optimization in particular is presented in each step of the iterative process a strictly convex approximating subproblem is generated and solved the generation of these subproblems is controlled by so called moving asymptotes which may both stabilize and speed up the convergence of the general process

decentralized adaptive output feedback stabilization for large scale stochastic nonlinear systems in this paper the problem of decentralized adaptive output feedback stabilization is investigated for large scale stochastic nonlinear systems with three types of uncertainties including parametric uncertainties nonlinear uncertain interactions and stochastic inverse dynamics under the assumption that the inverse dynamics of the subsystems are stochastic input to state stable an adaptive output feedback controller is constructively designed by the backstepping method it is shown that under some general conditions the closed loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability in addition the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin the contributions of the work are characterized by the following novel features 1 even for centralized single input single output systems this paper presents a first result in stochastic nonlinear adaptive output feedback asymptotic stabilization 2 the methodology previously developed for deterministic large scale systems is generalized to stochastic ones at the same time novel small gain conditions for small signals are identified in the setting of stochastic systems design 3 both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states 4 parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields which may appear nonlinearly 5 the concept of stochastic input to state stability and the method of changing supply functions are adapted for the first time to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control

a lyapunov based small gain theorem for interconnected switched systems abstract stability of an interconnected system consisting of two switched systems is investigated in the scenario where in both switched systems there may exist some subsystems that are not input to state stable non iss we show that providing the switching signals neither switch too frequently nor activate non iss subsystems for too long a small gain theorem can be used to conclude global asymptotic stability gas of the interconnected system for each switched system with the constraints on the switching signal being modeled by an auxiliary timer a correspondent hybrid system is defined to enable the construction of a hybrid iss lyapunov function apart from justifying the iss property of their corresponding switched systems these hybrid iss lyapunov functions are then combined to establish a lyapunov type small gain condition which guarantees that the interconnected system is globally asymptotically stable