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.
Cite
@article{arxiv.2602.14944,
title = {Pattern preservation in finite to infinite-horizon optimal control problems for dissipative systems},
author = {Matteo Della Rossa and Thiago Alves Lima and Lorenzo Freddi},
journal= {arXiv preprint arXiv:2602.14944},
year = {2026}
}