Control system design based on duality theorem

Abstract

This paper considers the finite dimensional approximation of dual problems that appear in control design problems, namely the discrete-time multi-objective el control problem and the continuous-time reference management problem for constrained systems. The dual problem is constructed with the properties that it does not have the duality gap with the primal problem, and that the space of variables is separable. The results are important for the exact computation of the optimal value. They provide an effective way to find separating hyperplanes between the feasible set and the level set of the cost functional.

Abstract linear programming approach to control problems - approximation theory

“…Theorem 1: Consider the dual problem (2), and define If we define T k as a sequence of convolution operators that approaches to the "delta" function, ı.e., then the constraint qualification (i) is fulfilled. This type of convolution operator appeared in [9].…”