Pattern preservation in finite to infinite-horizon optimal control problems for dissipative systems

Abstract

This paper focuses on infinite-horizon optimal control problems for dissipative systems and the relations to their finite-horizon formulations. We show that, for a large class of problems, dissipativity of the state equation, when a coercive storage function exists, implies that infinite-horizon optimal controls can be obtained as limits of the corresponding finite-horizon ones. This property is referred to as pattern preservation, or pattern-preserving property. Our analysis establishes a formal link between dissipativity theory and the variational convergence framework in optimal control, thus providing a concrete and numerically tractable condition for verifying pattern preservation. Numerical examples illustrate the effectiveness and limitations of the proposed sufficient conditions.

W.r.t. v1, improved presentation, weakened some technical hypotheses, discussion with related works