Maximum principle of optimal periodic control for functional differential systems (Q1066076)

This paper discusses the optimal periodic control problem to minimize the cost function \(J(u)=\int^{1}_{0}g(t,x(t),u(t))dt\), subject to the functional differential system \(dx(t)/dt=f(t,x_ t,u(t))\), \(x_ 1=x_ 0\), and \(u(\cdot)\in U_{ad}\). The maximum principle as a necessary condition of optimal control is proved under the assumption an associated equation and its adjoint both have no nontrivial periodic solution with period 1. In this paper, the control domain U is an arbitrary set in \(R^ m\).