Consistency of Primal-Dual Approximations for Convex Optimal Control Problems

Abstract

Problems in the optimal control of linear systems with convex costs are recast in a primal-dual (minimax) framework. An approximation scheme which leads to primal and dual optimal control problems n discrete time having similar structure to the original primal-dual pair is ntroduced. The discretizationis shown to be variationally consistent in the sense of epi/hypo-convergence, so that any limit point of solutions for the approximate minimax problems will solve the original primal and dual problems.