Safely Learning to Control the Constrained Linear Quadratic Regulator

TL;DR

This paper introduces a safe, data-driven control framework for constrained linear quadratic regulators with unknown dynamics, balancing safety and exploration through robust controller synthesis and non-asymptotic performance guarantees.

Contribution

It proposes a novel method for synthesizing robust, constraint-satisfying controllers using system level synthesis, ensuring safety during system identification.

Findings

Guarantees safety during exploration with unknown dynamics.

Provides non-asymptotic bounds on estimation and control performance.

Demonstrates effective system identification with persistent excitation.

Abstract

We study the constrained linear quadratic regulator with unknown dynamics, addressing the tension between safety and exploration in data-driven control techniques. We present a framework which allows for system identification through persistent excitation, while maintaining safety by guaranteeing the satisfaction of state and input constraints. This framework involves a novel method for synthesizing robust constraint-satisfying feedback controllers, leveraging newly developed tools from system level synthesis. We connect statistical results with cost sub-optimality bounds to give non-asymptotic guarantees on both estimation and controller performance.