Estimates of reachable sets of a nonlinear dynamical system with impulsive vector control and uncertainty

摘要

The problem of estimating the reachable sets of a nonlinear control dynamical system with uncertainty with respect to initial data is studied. It is assumed that the dynamic system has a special structure in which the nonlinear terms presented in dynamical equations are determined by quadratic forms with respect to the state coordinates, and we assume also that unknown initial states of the system belong to a given ellipsoid. It is assumed that in the system there are both classical measurable controls and generalized controls corresponding to the related vector measures. To estimate the reachable sets of a control system of this type and the reachable sets of the corresponding generalized nonlinear differential inclusions with vector measures, we use the results of the ellipsoidal estimation theory and the results of the theory of evolution equations for set-valued states of dynamical systems under uncertainty. Methods and algorithms for estimating reachable sets of a non-linear control system of the studied type are given in the paper; the results are illustrated by examples.