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The Power of Linear Controllers in LQR Control

Goel, Gautam and Hassibi, Babak (2020) The Power of Linear Controllers in LQR Control. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20200214-105627925

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Abstract

The Linear Quadratic Regulator (LQR) framework considers the problem of regulating a linear dynamical system perturbed by environmental noise. We compute the policy regret between three distinct control policies: i) the optimal online policy, whose linear structure is given by the Ricatti equations; ii) the optimal offline linear policy, which is the best linear state feedback policy given the noise sequence; and iii) the optimal offline policy, which selects the globally optimal control actions given the noise sequence. We fully characterize the optimal offline policy and show that it has a recursive form in terms of the optimal online policy and future disturbances. We also show that cost of the optimal offline linear policy converges to the cost of the optimal online policy as the time horizon grows large, and consequently the optimal offline linear policy incurs linear regret relative to the optimal offline policy, even in the optimistic setting where the noise is drawn i.i.d from a known distribution. Although we focus on the setting where the noise is stochastic, our results also imply new lower bounds on the policy regret achievable when the noise is chosen by an adaptive adversary.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2002.02574arXivDiscussion Paper
Additional Information:© 2020 G. Goel & B. Hassibi. To appear in Proceedings of Machine Learning Research.
Record Number:CaltechAUTHORS:20200214-105627925
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200214-105627925
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101309
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:14 Feb 2020 19:11
Last Modified:14 Feb 2020 19:11

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