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

TL;DR

This paper establishes a link between dissipativity in control systems and the convergence of finite-horizon optimal controls to infinite-horizon solutions, providing a practical way to verify pattern preservation.

Contribution

It introduces a formal connection between dissipativity theory and variational convergence, offering a new condition to verify pattern preservation in optimal control.

Findings

Finite-horizon controls converge to infinite-horizon solutions under dissipativity.

A numerically tractable condition for pattern preservation is proposed.

Numerical examples demonstrate the effectiveness and limitations of the approach.

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.