On the control synthesis for target problems in continuous and hybrid systems using level set methods

The focus of this paper is on the numerical solution of target control problems in continuous systems using level set methods. Such control problems appear naturally in hybrid control synthesis when specifications with respect to reachable states of the system are considered. To account for the existence of disturbance inputs the problem is studied as a pursuit-evasion differential game. The boundary of the reachable set, i.e. the set of states from which the problem is feasible, is characterized as the zero level set of the viscosity solution of a Hamilton-Jacobi PDE. Our contribution is the detailed presentation of the procedure for the computation of the control and worst-case disturbance policies together with the reachable set using level set methods.