Related papers: Competitive Control

Competitive Control

URL: http://arxiv.org/abs/2107.13657v2
Date: Fri, 30 Jul 2021 03:06:03 GMT
Title: Competitive Control
Authors: Gautam Goel and Babak Hassibi
Abstract summary: 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.
Score: 52.28457815067461
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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.

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