Optimization of Neutral Functional-Differential Inclusions

A Bolza problem of optimal control theory with a varying time interval given by convex, nonconvex functional-differential inclusions (P_N), (P_V) is considered. Our main goal is to derive sufficient optimality conditions for neutral functional-differential inclusions, which contain time delays in both state and velocity variables. Both state and endpoint constraints are involved. Presence of constraint conditions implies jump conditions for conjugate variable which are typical for such problems. Sufficient conditions under the t₁-transversality condition are proved incorporating the Euler–Lagrange- and Hamiltonian-type inclusions. As supplementary problems with discrete and discrete approximation inclusions (P_D), (P_DA) are considered and necessary, and sufficient conditions are given. The basic concept of obtaining optimality conditions is locally adjoint mappings and especially proved equivalence theorems. Furthermore, the application of these results is demonstrated by solving some illustrative examples.