Optimal control of evolution inclusions

We develop the method of discrete approximations for studying optimal control problems of the Bolza type for evolution systems governed by (generally nonconvex) differential inclusions in infinite-dimensional spaces. The results obtained involve well-posedness/stability of discrete approximations, necessary optimality conditions for general discrete-time systems, and necessary optimality conditions for continuous-time inclusions established in the extended Euler-Lagrange form. Our approach is based on the generalized differential constructions of variational analysis introduced earlier by the author.