Ellipsoidal Estimates of Reachable Sets for Control Systems with Nonlinear Terms

Abstract

The problem of estimating reachable sets of nonlinear dynamical control systems with quadratic nonlinearity and with uncertainty in initial states is studied. We assume that the uncertainty is of a set-membership kind when we know only the bounding set for unknown items and any additional statistical information on their behavior is not available. We present here approaches that allow finding ellipsoidal estimates of reachable sets which use the special structure of nonlinearity of studied control system. The algorithms of constructing such ellipsoidal set-valued estimates and numerical simulation results are given.