Competitive Control

TL;DR

This paper develops a competitive control framework that designs online controllers with optimal competitive ratios against offline optimal controllers, extending to nonlinear systems with MPC and demonstrating superior performance in experiments.

Contribution

It introduces a novel operator-theoretic approach for designing competitive controllers with optimal ratios, applicable to both linear and nonlinear systems, and provides computationally efficient solutions.

Findings

Optimal competitive controllers derived for finite and infinite horizons.

The competitive controller outperforms standard $H_2$ and $H_{ extinfty}$ controllers in MPC experiments.

Extension of competitive control to nonlinear systems using MPC.

Abstract

We consider control from the perspective of competitive analysis. Unlike much prior work on learning-based control, which focuses on minimizing regret against the best controller selected in hindsight from some specific class, we focus on designing an online controller which competes against a clairvoyant offline optimal controller. A natural performance metric in this setting is competitive ratio, which is the ratio between the cost incurred by the online controller and the cost incurred by the offline optimal controller. Using operator-theoretic techniques from robust control, we derive a computationally efficient state-space description of the the controller with optimal competitive ratio in both finite-horizon and infinite-horizon settings. We extend competitive control to nonlinear systems using Model Predictive Control (MPC) and present numerical experiments which show that our competitive controller can significantly outperform standard $H_2$ and $H_{\infty}$ controllers in the MPC setting.