LAUSR

This paper considers the minimisation problem of an integral functional with an integrand and a mixed nonconvex control constraint under some suitable conditions. We minimise the integral functional on the solution set of a control system described by nonlinear evolutionary inclusions with the mixed nonconvex control constraint, in which the left-hand side of the system contains the difference of two Clarke's Subdifferentials. We discuss a relaxation problem along with the original problem and show that the relaxation problem has an optimal solution, and for every optimal solution, there exists a minimising sequence of the original problem that converges to this solution concerning the trajectory, the control, and the functional.