Reinforcement learning for port-Hamiltonian systems

TL;DR

This paper integrates reinforcement learning with passivity-based control for port-Hamiltonian systems, enabling the design of near-optimal, robust controllers that satisfy energy-based stability criteria and include performance considerations.

Contribution

It introduces a reinforcement learning parameterization of energy-balancing passivity-based control that preserves PDE conditions and incorporates performance and robustness features.

Findings

Successfully applied to pendulum swing-up in simulations.

Generated near-optimal controllers with interpretability in energy terms.

Enhanced learning speed through system class parameterization.

Abstract

Passivity-based control (PBC) for port-Hamiltonian systems provides an intuitive way of achieving stabilization by rendering a system passive with respect to a desired storage function. However, in most instances the control law is obtained without any performance considerations and it has to be calculated by solving a complex partial differential equation (PDE). In order to address these issues we introduce a reinforcement learning approach into the energy-balancing passivity-based control (EB-PBC) method, which is a form of PBC in which the closed-loop energy is equal to the difference between the stored and supplied energies. We propose a technique to parameterize EB-PBC that preserves the systems's PDE matching conditions, does not require the specification of a global desired Hamiltonian, includes performance criteria, and is robust to extra non-linearities such as control input saturation. The parameters of the control law are found using actor-critic reinforcement learning, enabling learning near-optimal control policies satisfying a desired closed-loop energy landscape. The advantages are that near-optimal controllers can be generated using standard energy shaping techniques and that the solutions learned can be interpreted in terms of energy shaping and damping injection, which makes it possible to numerically assess stability using passivity theory. From the reinforcement learning perspective, our proposal allows for the class of port-Hamiltonian systems to be incorporated in the actor-critic framework, speeding up the learning thanks to the resulting parameterization of the policy. The method has been successfully applied to the pendulum swing-up problem in simulations and real-life experiments.