Stochastic Reinforcement Learning with Stability Guarantees for Control of Unknown Nonlinear Systems

TL;DR

This paper introduces a reinforcement learning algorithm that stabilizes unknown nonlinear systems by learning local linear dynamics and integrating this into neural policies, outperforming existing methods and providing theoretical stability guarantees.

Contribution

The paper presents a novel RL algorithm that guarantees stability for nonlinear systems by learning local linear models and incorporating them into control policies, with proven convergence and stability.

Findings

Outperforms SAC and PPO in stabilizing high-dimensional systems

Provides theoretical analysis of convergence and stability guarantees

Verifies asymptotic stability of learned control policies

Abstract

Designing a stabilizing controller for nonlinear systems is a challenging task, especially for high-dimensional problems with unknown dynamics. Traditional reinforcement learning algorithms applied to stabilization tasks tend to drive the system close to the equilibrium point. However, these approaches often fall short of achieving true stabilization and result in persistent oscillations around the equilibrium point. In this work, we propose a reinforcement learning algorithm that stabilizes the system by learning a local linear representation ofthe dynamics. The main component of the algorithm is integrating the learned gain matrix directly into the neural policy. We demonstrate the effectiveness of our algorithm on several challenging high-dimensional dynamical systems. In these simulations, our algorithm outperforms popular reinforcement learning algorithms, such as soft actor-critic (SAC) and proximal policy optimization (PPO), and successfully stabilizes the system. To support the numerical results, we provide a theoretical analysis of the feasibility of the learned algorithm for both deterministic and stochastic reinforcement learning settings, along with a convergence analysis of the proposed learning algorithm. Furthermore, we verify that the learned control policies indeed provide asymptotic stability for the nonlinear systems.