Differential Equations for Ellipsoidal Estimates of Reachable Sets for a Class of Control Systems with Nonlinearity and Uncertainty

Abstract

The problem of estimating reachable sets of nonlinear dynamical control systems with combined nonlinearity of quadratic and bilinear types and with uncertainty in initial states and in system parameters is studied. We assume that the uncertainty is of set-membership kind when only the bounding sets for unknown parameters and functions are given. We find the ellipsoidal estimates of reachable sets using the special bilinear-quadratic structure of studied control system. The main result consists in deriving the related differential equations which describe the dynamics of the ellipsoidal estimates of reachable sets of the control system under study, related numerical simulation results are also given. © 2018