Data-driven Bayesian Control of Port-Hamiltonian Systems

TL;DR

This paper introduces a data-driven Bayesian control method for Port-Hamiltonian systems using Gaussian Processes, enabling robust control with probabilistic stability guarantees based on uncertainty quantification.

Contribution

It presents a novel Gaussian Process-based control approach that leverages data to improve stability and performance of Port-Hamiltonian systems without relying solely on first-principles models.

Findings

Provides probabilistic stability guarantees for control.

Enables robust control using uncertainty quantification.

Improves performance over traditional model-based methods.

Abstract

Port-Hamiltonian theory is an established way to describe nonlinear physical systems widely used in various fields such as robotics, energy management, and mechanical engineering. This has led to considerable research interest in the control of Port-Hamiltonian systems, resulting in numerous model-based control techniques. However, the performance and stability of the closed-loop typically depend on the quality of the PH model, which is often difficult to obtain using first principles. We propose a Gaussian Processes (GP) based control approach for Port-Hamiltonian systems (GPC-PHS) by leveraging gathered data. The Bayesian characteristics of GPs enable the creation of a distribution encompassing all potential Hamiltonians instead of providing a singular point estimate. Using this uncertainty quantification, the proposed approach takes advantage of passivity-based robust control with interconnection and damping assignment to establish probabilistic stability guarantees.