Adaptive Control of Unknown Linear Switched Systems via Policy Gradient Methods

TL;DR

This paper develops a policy gradient adaptive control method for unknown linear switched systems, enabling real-time stabilization and tracking of switching dynamics under certain conditions.

Contribution

It introduces a PGAC approach for stabilizing unknown linear switched systems with theoretical guarantees and validation through simulations.

Findings

Policy gradient method stabilizes unknown switched systems.

The approach tracks switching dynamics under dwell time and small variation.

Simulations confirm theoretical stability and tracking performance.

Abstract

We consider the policy gradient adaptive control (PGAC) framework, which adaptively updates a control policy in real time, by performing data-based gradient descent steps on the linear quadratic regulator cost. This method has empirically shown to react to changing circumstances, such as model parameters, efficiently. To formalize this observation, we design a PGAC method which stabilizes linear switched systems, where both model parameters and switching time are unknown. We use sliding window data for the policy gradient estimate and show that under a dwell time condition and small dynamics variation, the policy can track the switching dynamics and ensure closed-loop stability. We perform simulations to validate our theoretical results.