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Published May 2021 | Submitted
Book Section - Chapter Open

Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting

Abstract

We study the problem of adaptive control in partially observable linear quadratic Gaussian control systems, where the model dynamics are unknown a priori. We propose LQGOPT, a novel adaptive control algorithm based on the principle of optimism in the face of uncertainty, to effectively minimize the overall control cost. We employ the predictor state evolution representation of the system dynamics and deploy a recently proposed closed-loop system identification method, estimation, and confidence bound construction. LQGOPT efficiently explores the system dynamics, estimates the model parameters up to their confidence interval, and deploys the controller of the most optimistic model for further exploration and exploitation. We provide stability guarantees for LQGOPT, and prove the first Õ(√T) regret upper bound for adaptive control of linear quadratic Gaussian (LQG) systems with convex cost, where T is the time horizon of the problem.

Additional Information

© 2021 AACC. S. Lale is supported in part by DARPA PAI and Beyond Limits Inc. B. Hassibi is supported in part by the National Science Foundation, by NASA's JPL through the President and Director's Fund. A. Anandkumar is supported in part by Bren endowed chair, DARPA PAI and LwLL grants, Microsoft, Google, and Adobe faculty fellowships.

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