Optimal state feedback for constrained nonlinear systems

Abstract

In this paper, we consider a general nonlinear control system that is subject to both terminal state and continuous inequality constraints. The continuous inequality constraints must be satisfied at every point in the time horizon—an infinite number of points. Our aim is to design an optimal feedback controller that yields efficient system performance and satisfaction of all constraints. We first formulate this problem as a semi-infinite optimization problem. We then show that, by using a novel exact penalty approach, this semi-infinite optimization problem can be converted into a sequence of nonlinear programming problems, each of which can be solved using standard numerical techniques. We conclude the paper with some convergence results.