A Maximum Principle for Optimal Control Problems with Neutral Functional Differential Systems

which have been studied extensively (as in [4]) and arise in many applications. The class of control problems considered include problems for which one wishes to minimize Jl x(t) at while requiring that u(t)EUCR, *G[0, T], and either x\ [T-h,T] He in a manifold in AC([T-h, T], R) or x(t) =f(*) on [T-h, T], f a fixed absolutely continuous function. These functional boundary conditions arise naturally since the "state" in neutral systems of the above type is a point in AC([-h, 0], R). Letao, toy and a be fixed in R with — <*> , 1 = [ao, a), I' — [/o, a)> For x continuous on I and t in ƒ', the notation F(x(-), t) will mean F is a functional in x, depending on any or all of the values tf(r),ao^T^. Fo r*G/ ' , l e t