2024/09/12 by Thanin Quartz, Quartz, Thanin, Ruikun Zhou +5 · 1 citation
Computer Science · #Adaptive Dynamic Programming Control #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Machine Learning (cs.LG) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2409.08382
openalex publication_date 2024/09/12 · openalex created_date 2024/10/23 · openalex updated_date 2026/07/28
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.