Optimization-based control by interconnection of nonlinear port-Hamiltonian systems

TL;DR

This paper introduces an optimization-based control method for nonlinear port-Hamiltonian systems, leveraging a port-Hamiltonian structure to ensure stability through a structure-preserving interconnection inspired by model predictive control.

Contribution

It formulates a novel control-by-interconnection approach using port-Hamiltonian systems and demonstrates stability of the interconnected system under certain observability conditions.

Findings

The interconnection stabilizes the nonlinear port-Hamiltonian system.

The control method preserves the port-Hamiltonian structure.

Numerical example confirms theoretical stability results.

Abstract

In this paper, we formulate an optimization-based control-by-interconnection approach to the stabilization problem of nonlinear port-Hamiltonian systems. Motivated by model predictive control, the feedback is defined as an initial part of a suboptimal solution of a finite horizon optimal control problem. To this end, we write the optimization method given by a primal-dual gradient dynamics arising from a possibly control-constrained optimal control problem as a port-Hamiltonian system. Then, using the port-Hamiltonian structure of the plant, we show that the MPC-type feedback law is indeed a structure-preserving interconnection of two port-Hamiltonian systems. We prove that, under an observability assumption, the interconnected system asymptotically stabilizes the plant dynamics. We illustrate the theoretical results by means of a numerical example.