A necessary condition for optimal control problem on a class of discontinuous dynamical systems

This paper concerns the optimal control problem for a class of the dynamical systems with the discontinuities. The vector field of the dynamical systems is represented as a combination of linear function and discontinuous sign function of state and control input. By virtue of Filippov regularization process and optimization results for differential inclusion systems, we establish a necessary condition of this discontinuous optimal control problem, which is a generation of classical Pontryagin´s Maximum principle.