Safely Learning to Control the Constrained Linear Quadratic Regulator
This addresses the challenge of balancing safety and exploration in data-driven control for constrained systems, offering a novel approach with theoretical guarantees.
The paper tackles the problem of safely learning to control a constrained linear quadratic regulator with unknown dynamics, presenting a framework that ensures safety while exploring, and provides non-asymptotic guarantees on estimation and controller performance.
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.