on switching h controllers for a class of linear parameter varying systems abstract we consider switching h controllers for a class of linear parameter varying lpv systems scheduled along a measurable parameter trajectory the candidate controllers are selected from a given controller set according to the switching rules based on the scheduling variable we provide sufficient conditions to guarantee the stability of the switching lpv systems in terms of the dwell time and the average dwell time our results are illustrated with an example where switching between two robust controllers is performed for an lpv system

uniform stability of switched linear systems extensions of lasalle s invariance principle this paper addresses the uniform stability of switched linear systems where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set we provide a collection of results that can be viewed as extensions of lasalle s invariance principle to certain classes of switched linear systems using these results one can deduce asymptotic stability using multiple lyapunov functions whose lie derivatives are only negative semidefinite depending on the regularity assumptions placed on the switching signals one may be able to conclude just asymptotic stability or uniform exponential stability we show by counter example that the results obtained are tight

fast gain scheduling on tracking problems using derivative information current gain scheduling practice is necessarily limited to slow variation in scheduling variables this paper proposes a control law which reflects the exogenous signal and its time derivative with assumption of its availability the proposed controller achieves better performance than the existents for tracking fast scheduling variables while rejecting exogenous signal

stability results for switched controller systems there are many practical control problems where the control action is determined by switching among a given set of control laws this paper presents necessary and sufficient conditions to test for quadratic stabilizability and for robust stabilizability with a quadratic storage function for switched controller systems algorithms which can be used to construct appropriately stabilizing control laws are also presented

on a stability theorem for nonlinear systems with slowly varying inputs recently m kelemen ieee trans automat contr vol ac 31 766 768 aug 1986 presented a stability result that deals with the response of a nonlinear system to slowly varying input signals in this work a proof is given under a weaker hypothesis on the input signal by constructing a lyapunov function that is standard in the control literature this proof may be more accessible than the other approaches for completeness brief proofs of some intermediate results that are regarded as well known are included a simple example is given to show that this approach can yield explicit bounds in certain situations of interest

brief paper robust output feedback stabilizability via controller switching the paper considers the output feedback robust stabilizability problem for uncertain dynamical systems the uncertain system under consideration is a composite of a continuous time plant and a switched controller a necessary and sufficient condition of absolute stabilizability is given in terms of the existense of suitable solutions to a dynamic programming equation and a riccati algebraic equation of the h filtering type a real time implementable method for robust stabilization is also presented

improved stability analysis and gain scheduled controller synthesis for parameter dependent systems we present new algorithms for robust stability analysis and gain scheduled controller synthesis for linear systems affected by time varying parametric uncertainties these new techniques can also be applied to parameter dependent nonlinear systems with real rational nonlinearities sufficient conditions for robust stability as well as conditions for the existence of a robustly stabilizing gain scheduled controller are given in terms of a finite number of linear matrix inequalities lmis explicit formulas for constructing robustly stabilizing gain scheduled controllers are given in terms of the feasible set of these lmis the improvement offered by our approach over existing methods for stability analysis and gain scheduled controller synthesis for parameter dependent linear systems are analyzed in theory numerical examples demonstrate that our approach can offer significant improvement in practice

bounded amplitude performance of switched lpv systems with applications to hybrid systems this paper discusses recent results on multiple linear agent control for systems satisfying a bounded amplitude performance constraint the plant is assumed to be a linear parameter varying lpv system scheduled along a nominal parameter trajectory in this respect the control problem represents a plant operating between a prespecified set of operating conditions linear controllers are designed at setpoints along this scheduling trajectory to satisfy bounded amplitude performance constraints this paper discusses an approach to analyze the switched system behavior under practical assumptions on the structure of the switching rule the approach combines the scheduling parameter with lpv system properties to derive bounds on the switching behavior of the system these estimates are then used to construct a logical model of the switched system behavior in the form of a timed automaton in this respect this paper presents a way of extracting logical models of continuous time system behavior

on uniform stabilization of discrete time linear parameter varying control systems for discrete time polytopic linear parameter varying systems the uniform exponential stability which is equivalent to the asymptotic stability and includes the quadratic stability as a special case is characterized by the union of an increasing family of linear matrix inequality conditions on the other hand in certain cases nonconservative synthesis of uniformly stabilizing controllers is achieved via a system of finite number of linear matrix inequalities if the controller is allowed to have finite memory of past parameters two such cases are robust state feedback in a relaxed sense against polytopic parameter variations and multiple output injections under polytopic fusion rules

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

nonlinear optimal control as quantum mechanical eigenvalue problems a novel approach for approximating the nonlinear optimal feedback control of a system with a terminal cost is proposed to lessen the difficulty due to nonlinearity we try to treat the system in a framework of linear theories for this we assume a quantum mechanical linear wave associated with the system since the control system is constrained by state equations we handle the system according to quantum mechanics of constrained dynamics a hamiltonian is represented as a linear operator acting on a function that describes behavior of waves subsequently nonlinear feedback is calculated without any time integration in the backward direction using eigenvalues and eigenfunctions of the linear hamiltonian operator an optimal feedback law is given as a combination of analytic functions of time and state variables we take as an example a system described by two scalar variables for state and control input simulation studies on the system by the eigenvalue analysis show that the proposed method reduces calculation time to nearly a tenth that of a numerical calculation of a hamilton jacobi equation by a finite difference method

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

a parameter set division and switching gain scheduling controllers design method for time varying plants abstract this paper presents a new technique to design switching gain scheduling controllers for plants with measurable time varying parameters by dividing the parameter set into a sufficient number of subsets and by designing a robust controller to each subset the designed switching gain scheduling controllers achieve a desired l 2 gain performance for each subset while ensuring stability whenever a controller switching occurs due to the crossing of the time varying parameters between any two adjacent subsets based on integral quadratic constraints theory and lyapunov stability theory a switching gain scheduling controllers design problem amounts to solving optimization problems each optimization problem is to be solved by a combination of the bisection search and the numerical nonsmooth optimization method the main advantage of the proposed technique is that the division of the parameter region is determined automatically without any prespecified parameter set division which is required in most of previously developed switching gain scheduling controllers design methods a numerical example illustrates the validity of the proposed technique

an example of a nonlinear regulator the purpose of this note is to use the concept of feedback equivalence to linear controllable systems in order to design a nonlinear regulator for a synchronous generator connected to an infinite bus the design of the regulator will show how recently developed theorems in the area of geometric nonlinear control theory approach a power system problem offering an interesting solution

solutions to the hamilton jacobi equation with algebraic gradients in this paper the hamilton jacobi equation hje with coefficients consisting of rational functions is considered and its solutions with algebraic gradients are characterized in terms of commutative algebra it is shown that there exists a solution with an algebraic gradient if and only if an involutive maximal ideal containing the hamiltonian exists in a polynomial ring over the rational function field if such an ideal is found the gradient of the solution is defined implicitly by a set of algebraic equations then the gradient is determined by solving the set of algebraic equations pointwise without storing the solution over a domain in the state space thus the so called curse of dimensionality can be removed when a solution to the hje with an algebraic gradient exists new classes of explicit solutions for a nonlinear optimal regulator problem are given as applications of the present approach

switching lpv control designs using multiple parameter dependent lyapunov functions in this paper we study the switching control of linear parameter varying lpv systems using multiple parameter dependent lyapunov functions to improve performance and enhance control design flexibility a family of lpv controllers is designed each suitable for a specific parameter subregion they are switched so that the closed loop system remains stable and its performance is optimized two switching logics hysteresis switching and switching with average dwell time are examined the control synthesis conditions for both switching logics are formulated as matrix optimization problems which are generally non convex but can be convexified under some simplifying assumptions the hysteresis switching lpv control scheme is then applied to an active magnetic bearing problem

d dimensional dependence functions and archimax copulas we introduce a new class of dependence functions and method for constructing tail and pickands dependence functions finally we conjecture the structure of d dimensional archimax copulas and discuss some classes of d dimensional archimax copulas

discrete time high order schemes for viscosity solutions of hamilton jacobi bellman equations a general method for constructing high order approximation schemes for hamilton jacobi bellman equations is given the method is based on a discrete version of the dynamic programming principle we prove a general convergence result for this class of approximation schemes also obtaining under more restrictive assumptions an estimate in l infty of the order of convergence and of the local truncation error the schemes can be applied in particular to the stationary linear first order equation in bbb r n we present several examples of schemes belonging to this class and with fast convergence to the solution

uniform stabilization of discrete time switched and markovian jump linear systems the uniform stability of discrete time switched linear systems possibly with a strongly connected switching path constraint and the existence of finite path dependent dynamic output feedback controllers uniformly stabilizing such a system are both shown to be characterized by the existence of a finite dimensional feasible system of linear matrix inequalities this characterization is based on the observation that a linear time varying system is uniformly stable only if there exists a finite path dependent quadratic lyapunov function the synthesis of a uniformly stabilizing controller is done without conservatism by solving any feasible system of linear matrix inequalities among an increasing family of systems of linear matrix inequalities the result carries over to the almost sure uniform stabilization of markovian jump linear systems

on deterministic control problems an approximation procedure for the optimal cost i the stationary problem we study deterministic optimal control problems having stopping time continuous and impulse controls in each strategy we obtain the optimal cost considered as the maximum element of a suitable set of subsolutions of the associated hamilton jacobi equation using an approximation method a particular derivative discretization scheme is employed convergence of approximate solutions is shown taking advantage of a discrete maximum principle which is also proved for the numerical solutions of approximate problems we use a method of relaxation type the algorithm is very simple it can be run on computers with small central memory in part i we study the stationary case in part ii siam j control optim 23 1985 pp 267 285 we study the nonstationary case

on the α migrativity of multivariate semi copulas in this paper we introduce and study the a migrative property for the class of multivariate semi copulas in particular a characterization of a migrative copulas is provided

feedback control of nonlinear systems by extended linearization for single input multiple output nonlinear systems we consider a design method based on the family of linearizations of the system parameterized by constant operating points nonlinear state feedback control laws and observer state feedback control laws are designed such that the eigenvalues of the family of linearized closed loop systems are placed at specified values that are locally invariant with respect to the closed loop operating point the method is illustrated by application to the problem of automatically balancing an inverted pendulum

2 increasing binary aggregation operators abstract in this work we investigate the class of binary aggregation operators agops satisfying the 2 increasing property obtaining some characterizations for agops having other special properties e g quasi arithmetic mean choquet integral based modularity and presenting some construction methods in particular the notion of p increasing function is used in order to characterize the composition of 2 increasing agops the lattice structure with respect to the pointwise order of some subclasses of 2 increasing agops is presented finally a method is given for constructing copulas beginning from 2 increasing and 1 lipschitz agops

global transformations of nonlinear systems recent results have established necessary and sufficient conditions for a nonlinear system of the form dot x t f x t u t g x t with f 0 0 to be locally equivalent in a neighborhood of the origin in rnto a controllable linear system we combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system in doing so we introduce a technique for constructing a transformation under the assumptions that g ldot f dotg ad n 1 f ldotg span an n dimensional space and that g ldot f ldot g ad n 2 f ldotg is an involutive set

on representations of 2 increasing binary aggregation functions in this paper we provide two different representations of 2 increasing binary aggregation functions by means of their lower and upper margins and a suitable copula

hybrid dynamical systems robust control synthesis problems the paper presents a new approach to robust control synthesis problems for hybrid dynamical systems the hybrid system under consideration is a composite of a continuous plant and a discrete event controller state and output feedback problems are considered the main results are given in terms of the existence of suitable solutions to a dynamic programming equation and a riccati differential equation of the h filtering type these results show a connection between the theories of hybrid dynamical systems and robust and nonlinear control

a supervised switching control policy for lpv systems with inaccurate parameter knowledge this technical note deals with the switched supervised control of linear parameter varying systems whose parameters values are online acquirable only with an arbitrarily large degree of uncertainty the purpose is to define a switching policy inside a family of predesigned controllers so that the switched closed loop system result to be exponentially stable the proposed switching logic is based on a performance evaluation criterion which uses a measurable lyapunov like functional of the output the exponential stability condition is derived imposing a sufficient long time interval over which the functional is decreasing an interesting feature of the technical note is that no particular structure on the kind of uncertainty affecting the parameter values is assumed

brief lpv systems with parameter varying time delays analysis and control in this paper we address the analysis and state feedback synthesis problems for linear parameter varying lpv systems with parameter varying time delays it is assumed that the state space data and the time delays are dependent on parameters that are measurable in real time and vary in a compact set with bounded variation rates we explore the stability and the induced l 2 norm performance of these systems using parameter dependent lyapunov functionals in addition the design of parameter dependent state feedback controllers that guarantee desired l 2 gain performance is examined both analysis and synthesis conditions are formulated in terms of linear matrix inequalities lmis that can be solved via efficient interior point algorithms

on a comparison between mahalanobis distance and choquet integral the choquet mahalanobis operator mahalanobis distance can be used in problems where variables are not independent the presence of the covariance matrix in this expression permits us to represent the dependence between the variables fuzzy measures and choquet integrals have a similar purpose in this paper we compare these two expressions to do so in the proper setting we introduce a choquet integral based distance then we consider probability density functions based on these two distances in particular we review the gaussian distribution which is based on the mahalanobis distance and introduce another distribution based on the choquet distance then we introduce an operator that generalizes the choquet integral and the mahalanobis distance it is the choquet mahalanobis integral some propositions are also proven establishing equivalences and links between the choquet mahalanobis integral the choquet integral and the mahalanobis distance

stabilization of a class of nonlinear systems by a smooth feedback control we consider the stabilizability problem for systems of the form x f x ub in the neighborhood of an equilibrium point of f x first by means of center manifold theory a lower order system is introduced if this system is stabilizable then so is the original system results on the stabilization of the low order system are presented no resort is taken to liapunov theory the relation between stabilizability and controllability is discussed

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

incremental h control for switched nonlinear systems abstract in this paper we investigate the incremental h control for switched nonlinear systems by using a state dependent switching law and an average dwell time approach incorporated with multiple lyapunov functions even if all subsystems are unstable a sufficient condition for the incremental h control problem to be solvable is derived based on the design state dependent switching law furthermore when all subsystems are incrementally globally asymptotically stable igas the switched nonlinear system under the average dwell time scheme is igas and possesses a weighted incremental l2 gain then we extend this result to the case where both igas subsystems and unstable subsystems coexist if the activation time ratio between igas subsystems and unstable ones is not less than a specified constant sufficient conditions for the weighted incremental h performance of the switched system are guaranteed two numerical examples are given to illustrate the validity of the proposed approach

1 lipschitz power stable aggregation functions in this paper we study the structure of the class of all binary 1 lipschitz power stable aggregation functions a special attention is devoted to the characterization of power stable quasi copulas moreover the relations between copulas and quasi copulas as 1 lipschitz aggregation functions with neutral element e 1 sup and inf closures of copulas and track defined functions based on copulas in the framework of binary power stable aggregation functions are characterized

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

characterizing isometries on the order polytope with an application to the theory of fuzzy measures in this paper we study the group of isometries over the order polytope of a poset we provide a result that characterizes any isometry based on the order structure in the original poset from this result we provide upper bounds for the number of isometries over the order polytope in terms of its number of connected components finally as an example of application we recover the set of isometries for the polytope of fuzzy measures and the polytope of p symmetric measures when the indifference partition is fixed

guaranteed properties of gain scheduled control for linear parameter varying plants abstract gain scheduling has proven to be a successful design methodology in many engineering applications however in the absence of a sound theoretical analysis these designs come with no guarantees on the robustness performance or even nominal stability of the overall gain scheduled design this paper presents such an analysis for one type of gain scheduled system namely a linear parameter varying plant scheduling on its exogenous parameters conditions are given which guarantee that the stability robustness and performance properties of the fixed operating point designs carry over to the global gain scheduled design these conditions confirm and formalize popular notions regarding gain scheduled design such as the scheduling variable should vary slowly

brief stability and l2 gain properties of lpv systems stability and l 2 gain properties of linear parameter varying systems are obtained under assumed bounds on either the maximum or average value of the parameter rate

galerkin approximations of the generalized hamilton jacobi bellman equation in this paper we study the convergence of the galerkin approximation method applied to the generalized hamilton jacobi bellman ghjb equation over a compact set containing the origin the ghjb equation gives the cost of an arbitrary control law and can be used to improve the performance of this control the ghjb equation can also be used to successively approximate the hamilton jacobi bellman equation we state sufficient conditions that guarantee that the galerkin approximation converges to the solution of the ghjb equation and that the resulting approximate control is stabilizing on the same region as the initial control the method is demonstrated on a simple nonlinear system and is compared to a result obtained by using exact feedback linearization in conjunction with the lqr design method

on a family of multivariate copulas for aggregation processes we introduce a family of multivariate copulas a special type of n ary aggregation operations depending on a univariate function this family is used in the construction of a special aggregation operation that satisfies a lipschitz condition several examples are provided and some statistical properties are studied