Manifold turnpikes of nonlinear port-Hamiltonian descriptor systems under minimal energy supply

TL;DR

This paper investigates the turnpike phenomenon in nonlinear port-Hamiltonian descriptor systems with minimal energy supply, demonstrating that optimal controls tend to stay near a specific manifold under certain conditions.

Contribution

It establishes the manifold turnpike property for nonlinear port-Hamiltonian systems, extending the understanding of optimal control behavior in these systems under minimal energy constraints.

Findings

Optimal control problems are dissipative with respect to a manifold.

Under controllability, the system exhibits a manifold turnpike property.

The results depend on smoothness assumptions of system nonlinearities.

Abstract

Turnpike phenomena of nonlinear port-Hamiltonian descriptor systems under minimal energy supply are studied. Under assumptions on the smoothness of the system nonlinearities, it is shown that the optimal control problem is dissipative with respect to a manifold. Then, under controllability assumptions, it is shown that the optimal control problem exhibits a manifold turnpike property.