Exterior penalty in optimal control problem with state-control constraints

Abstract

We consider an abstract optimal control problem with additional equality and inequality state and control constraints, we use the exterior penalty function to transform the constrained optimal control problem into a sequence of unconstrained optimal control problems, under conditions in control lie in L 1 , the sequence of the solution to the unconstrained problem contains a subsequence converging of the solution of constrained problem, this convergence is strong when the problem is non convex, and is weak if the problem is convex in control. This generalizes the results of P.Nepomiastcthy [4] where he considered the control in the Hilbert space L 2 (I, R m ).

Optimal Control with Time Delays via the Penalty Method

“…Now we prove existence of an optimal solution to more general problems of optimal control with time delays. The result is obtained via the exterior penalty method [1,12] and Theorem 2.4. The optimal control problem with time delays is defined as follows:…”