Ellipsoidal estimates of reachable sets of impulsive control problems under uncertainty

Abstract

For impulsive control systems with uncertainty in initial states and in the system parameters the problem of estimating reachable sets is studied. The initial states are taken to be unknown but bounded with given bounds. Also the matrix included in the differential equations of the system dynamics is uncertain and only bounds on admissible values of this matrix coefficients are known. The problem is considered under additional constraint on the system states. It is assumed that the system states should belong to the given ellipsoid in the state space. We present here the state estimation algorithms that use the special structure of the bilinear impulsive control system and take into account additional restrictions on states and controls. The algorithms are based on ellipsoidal techniques for estimating the trajectory tubes of uncertain dynamical systems.