Robust Model-Free Learning and Control without Prior Knowledge

TL;DR

This paper introduces a simple, model-free control algorithm capable of robustly stabilizing unknown linear systems with bounded disturbances, without prior system knowledge, ensuring stability and providing explicit bounds.

Contribution

It presents the first model-free control method with robust stability guarantees that does not rely on any prior assumptions about the system dynamics or disturbances.

Findings

Guarantees robust stability under arbitrary bounded disturbances

Provides asymptotic and worst-case bounds on trajectories

Demonstrates good performance in simulations

Abstract

We present a simple model-free control algorithm that is able to robustly learn and stabilize an unknown discrete-time linear system with full control and state feedback subject to arbitrary bounded disturbance and noise sequences. The controller does not require any prior knowledge of the system dynamics, disturbances, or noise, yet it can guarantee robust stability and provides asymptotic and worst-case bounds on the state and input trajectories. To the best of our knowledge, this is the first model-free algorithm that comes with such robust stability guarantees without the need to make any prior assumptions about the system. We would like to highlight the new convex geometry-based approach taken towards robust stability analysis which served as a key enabler in our results. We will conclude with simulation results that show that despite the generality and simplicity, the controller demonstrates good closed-loop performance.