Stabilizing Dynamical Systems via Policy Gradient Methods

• URL: http://arxiv.org/abs/2110.06418v1
• Date: Wed, 13 Oct 2021 00:58:57 GMT
• Title: Stabilizing Dynamical Systems via Policy Gradient Methods
• Authors: Juan C. Perdomo and Jack Umenberger and Max Simchowitz
• Abstract summary: We provide a model-free algorithm for stabilizing fully observed dynamical systems. We prove that this method efficiently recovers a stabilizing controller for linear systems. We empirically evaluate the effectiveness of our approach on common control benchmarks.
• Score: 32.88312419270879
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Stabilizing an unknown control system is one of the most fundamental problems in control systems engineering. In this paper, we provide a simple, model-free algorithm for stabilizing fully observed dynamical systems. While model-free methods have become increasingly popular in practice due to their simplicity and flexibility, stabilization via direct policy search has received surprisingly little attention. Our algorithm proceeds by solving a series of discounted LQR problems, where the discount factor is gradually increased. We prove that this method efficiently recovers a stabilizing controller for linear systems, and for smooth, nonlinear systems within a neighborhood of their equilibria. Our approach overcomes a significant limitation of prior work, namely the need for a pre-given stabilizing control policy. We empirically evaluate the effectiveness of our approach on common control benchmarks.

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