Bayesian Algorithms Learn to Stabilize Unknown Continuous-Time Systems

TL;DR

This paper introduces a Bayesian learning algorithm designed to stabilize unknown continuous-time stochastic linear systems quickly and effectively, addressing a critical gap in control of uncertain dynamical systems.

Contribution

The paper presents a novel Bayesian stabilization algorithm that learns to control unknown continuous-time systems within finite time, improving upon existing methods.

Findings

Effective stabilization achieved after short interaction periods.

Algorithm reliably learns system dynamics and stabilizes in finite time.

Demonstrates practical applicability to uncertain linear systems.

Abstract

Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true dynamics matrices are unknown and need to be learned from the observed data of state trajectory. An important issue is to ensure that the system is stabilized and destabilizing control actions due to model uncertainties are precluded as soon as possible. A reliable stabilization procedure for this purpose that can effectively learn from unstable data to stabilize the system in a finite time is not currently available. In this work, we propose a novel Bayesian learning algorithm that stabilizes unknown continuous-time stochastic linear systems. The presented algorithm is flexible and exposes effective stabilization performance after a remarkably short time period of interacting with the system.