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Finite-time System Identification and Adaptive Control in Autoregressive Exogenous Systems

Lale, Sahin and Azizzadenesheli, Kamyar and Hassibi, Babak and Anandkumar, Animashree (2021) Finite-time System Identification and Adaptive Control in Autoregressive Exogenous Systems. Proceedings of Machine Learning Research, 144 . pp. 967-979. ISSN 1938-7228. https://resolver.caltech.edu/CaltechAUTHORS:20210727-162630002

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Abstract

Autoregressive exogenous (ARX) systems are the general class of input-output dynamical system used for modeling stochastic linear dynamical system (LDS) including partially observable LDS such as LQG systems. In this work, we study the problem of system identification and adaptive control of unknown ARX systems. We provide finite-time learning guarantees for the ARX systems under both open-loop and closed-loop data collection. Using these guarantees, we design adaptive control algorithms for unknown ARX systems with arbitrary strongly convex or non-strongly convex quadratic regulating costs. Under strongly convex cost functions, we design an adaptive control algorithm based on online gradient descent to design and update the controllers that are constructed via a convex controller reparametrization. We show that our algorithm has Õ(√T) regret via explore and commit approach and if the model estimates are updated in epochs using closed-loop data collection, it attains the optimal regret of polylog(T) after T time-steps of interaction. For the case of non-strongly convex quadratic cost functions, we propose an adaptive control algorithm that deploys the optimism in the face of uncertainty principle to design the controller. In this setting, we show that the explore and commit approach has a regret upper bound of Õ(√T^(2/3)), and the adaptive control with continuous model estimate updates attains Õ(√T) regret after T time-steps.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://proceedings.mlr.press/v144/lale21b.htmlPublisherArticle
ORCID:
AuthorORCID
Azizzadenesheli, Kamyar0000-0001-8507-1868
Additional Information:© 2021 S. Lale, K. Azizzadenesheli, B. Hassibi & A. Anandkumar.
Subject Keywords:ARX systems, system identification, adaptive control, regret
Record Number:CaltechAUTHORS:20210727-162630002
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210727-162630002
Official Citation:Lale, S., Azizzadenesheli, K., Hassibi, B., Anandkumar, A. (2021). Finite-time System Identification and Adaptive Control in Autoregressive Exogenous Systems. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research; 144:967-979. Available from http://proceedings.mlr.press/v144/lale21b.html.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110023
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:02 Aug 2021 17:27
Last Modified:02 Aug 2021 17:27

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