Algorithms of Estimating Reachable Sets of Nonlinear Control Systems with Uncertainty

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 approaches that allow finding ellipsoidal estimates of reachable sets. The algorithms of constructing such ellipsoidal set-valued estimates and numerical simulation results are given in two cases, for control systems with classical controls and for measure driven (impulsive) control systems.