Neural Energy Casimir Control for Port-Hamiltonian Systems

TL;DR

This paper introduces a neural network framework to learn energy Casimir and Lyapunov functions for port-Hamiltonian systems, enabling effective stabilization at desired equilibria with reduced computational complexity.

Contribution

It proposes a novel neural network-based approach for computing Casimir and Lyapunov functions, facilitating equilibrium assignment and stability analysis in port-Hamiltonian systems.

Findings

Neural network approach successfully learns Casimir and Lyapunov functions.

Regularization enables equilibrium assignment in training.

Distance to desired equilibrium decreases linearly with training loss.

Abstract

The energy Casimir method is an effective controller design approach to stabilize port-Hamiltonian systems at a desired equilibrium. However, its application relies on the availability of suitable Casimir and Lyapunov functions, whose computation are generally intractable. In this paper, we propose a neural network-based framework to learn these functions. We show how to achieve equilibrium assignment by adding suitable regularization terms in the training cost. We also propose a parameterization of Casimir functions for reducing the training complexity. Moreover, the distance between the equilibrium of the learned Lyapunov function and the desired equilibrium is analyzed, which indicates that for small suboptimality gaps, the distance decreases linearly with respect to the training loss. Our methods are backed up by simulations on a pendulum system.