Data-Driven Boundary Control of Distributed Port-Hamiltonian Systems

TL;DR

This paper introduces a data-driven approach combining Gaussian Process modeling with boundary control for distributed port-Hamiltonian systems, enabling robust control despite unknown or nonlinear dynamics.

Contribution

It proposes a novel method that learns the Hamiltonian structure from data and incorporates uncertainty into boundary control for improved robustness.

Findings

The approach successfully bounds system trajectories under model uncertainty.

Application to a simulated shallow water system demonstrates effectiveness.

Probabilistic conditions ensure stability despite partial model knowledge.

Abstract

Distributed Port-Hamiltonian (dPHS) theory provides a powerful framework for modeling physical systems governed by partial differential equations and has enabled a broad class of boundary control methodologies. Their effectiveness, however, relies heavily on the availability of accurate system models, which may be difficult to obtain in the presence of nonlinear and partially unknown dynamics. To address this challenge, we combine Gaussian Process distributed Port-Hamiltonian system (GP-dPHS) learning with boundary control by interconnection. The GP-dPHS model is used to infer the unknown Hamiltonian structure from data, while its posterior uncertainty is incorporated into an energy-based robustness analysis. This yields probabilistic conditions under which the closed-loop trajectories remain bounded despite model mismatch. The method is illustrated on a simulated shallow water system.