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

We consider techniques of estimating trajectory tubes of nonlinear control systems with uncertainty in the initial data and under the assumption of a quadratic nonlinearity of system state velocities over the states of the system. It is assumed that the uncertain initial states and the admissible controls are constrained by ellipsoidal restrictions. We study problems of sensitivity of reachable sets and of their ellipsoidal estimates to finite-dimensional parameters appearing in the constraints and in the uncertain dynamics of the control system. The results are based on algorithms and techniques of the ellipsoidal estimation theory and on the theory of differential inclusions.