Approximation Techniques in Impulsive Control Problems for the Tubes of Solutions of Uncertain Differential Systems

Abstract

The paper deals with the control problems for the system described by differential equations containing impulsive terms (or measures). The problem is studied under uncertainty conditions with set-membership description of uncertain variables, which are taken to be unknown but bounded with given bounds (e.g., the model may contain unpredictable errors without their statistical description). The main problem is to find external and internal estimates for set-valued states of nonlinear dynamical impulsive control systems and related nonlinear differential inclusions with uncertain initial state. Basing on the techniques of approximation of the generalized trajectory tubes by the solutions of usual differential systems without measure terms and using the techniques of ellipsoidal calculus we present here a new state estimation algorithms for the studied impulsive control problem. The examples of construction of such ellipsoidal estimates of reachable sets and trajectory tubes of impulsive control systems are given.