Optimal control of semilinear unbounded differential inclusions

This paper concerns a general optimal control problem of the Mayer type for semilinear unbounded differential inclusions with endpoint constraints in reflexive and separable Banach spaces. Based on the method of discrete approximations and advanced generalized differential tools of variational analysis, we establish necessary optimality conditions for discrete-time control problems and then, by passing to the limit, derive intrinsic optimality conditions of the extended Euler-Lagrange type for semilinear evolution inclusions.