Control system design using duality theorem

Abstract

Many control system design problems are cast as an infinite-dimensional linear programming, where one of the main focus is how to approximate it by a finite-dimensional problem. This paper discusses a finite-dimensional approximation of the primal-dual approach. Unlike the finite-dimensional counterpart, the optimal costs for the primal and dual problems may have duality gap. This paper provides a way to approximate the dual of the continuous-time reference management problem, and show that the gap-free approximation is possible.