Abstract

The state estimation problem for uncertain impulsive control systems with a special structure is considered. The initial states are taken to be unknown but bounded with given bounds. We assume here that the coefficients of the matrix included in the differential equations are not exactly known, but belong to the given compact set in the corresponding space. We present here algorithms that allow to find the external ellipsoidal estimates of reachable sets for such bilinear impulsive uncertain systems.

Highlights

  • 1 Introduction The paper deals with an impulsive control systems with unknown but bounded uncertainties related to the case of a set-membership description of uncertainty [Kurzhanski and Valyi, 1997; Schweppe, 1973; Walter and Pronzato, 1997; Boyd, El Ghaoui, Feron and Balakrishnan, 1994]

  • The main problem considered in this paper is to find the external ellipsoidal estimates for reachable sets X (t) of the dynamic control systems (1)–(5) with uncertain matrix of the system and uncertain initial state basing on the special structure of the data A, U, V and X0

  • At the end of the process we will get the external estimate E(a+(T ), Q+(T )) of the reachable set X (T ) of the impulsive control system (1)–(5) with uncertain matrix of the system and uncertain initial state basing on the special structure of the data A, U and X0

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Summary

Introduction

The paper deals with an impulsive control systems with unknown but bounded uncertainties related to the case of a set-membership description of uncertainty [Kurzhanski and Valyi, 1997; Schweppe, 1973; Walter and Pronzato, 1997; Boyd, El Ghaoui, Feron and Balakrishnan, 1994]. Systems with such uncertainties may be found in many applied areas such as engineering problems in physics and cybernetics [Ceccarelli and etc., 2006], economics, biological and ecological modeling when it occurs that a stochastic nature of errors is questionable. The algorithms of constructing external ellipsoidal estimates for studied systems are given

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