Discrete approximations and necessary optimality conditions for functional-differential inclusions of neutral type

This paper deals with necessary optimality conditions for optimal control systems governed by constrained functional-differential inclusions of neutral type. While some results are available for smooth control systems governed by neutral functional-differential equations, we are not familiar with any results for neutral functional-differential inclusions, even with smooth cost functionals in the absence of endpoint constraints. Developing the method of discrete approximations and employing advanced tools of generalized differentiation, we conduct a variational analysis of neutral functional-differential inclusions and obtain new necessary optimality conditions of both Euler-Lagrange and Hamiltonian types.