Construction of set-valued estimates of reachable sets for some nonlinear dynamical systems with impulsive control

A method of constructing ellipsoidal estimates of reachable sets is proposed for a nonlinear system with a scalar impulsive control and uncertainty in initial data. A special discontinuous change of time is used to transform the impulsive system under consideration into an ordinary differential inclusion without impulsive components. To estimate reachable sets of the obtained nonlinear differential inclusion, results from the theory of ellipsoidal estimation and theory of evolution equations of set-valued states of dynamical systems under uncertainty are used.