Estimates of reachable sets of control systems with nonlinearity and parametric perturbations

Abstract

We consider estimation techniques for trajectory tubes of a nonlinear control system with uncertainty in the initial data and under the assumption of quadratic nonlinearity of the velocity vectors with respect to the states of the system. It is assumed that the uncertain initial states and admissible controls are subject to ellipsoidal constraints. We study problems of sensitivity of reachable sets and of their ellipsoidal estimates to a finite-dimensional parameter appearing in the constraints and in the dynamics of the uncertain control system. The results are based on algorithms and techniques of the theory of ellipsoidal estimation and the theory of differential inclusions.