Value iteration and adaptive optimal output regulation with assured convergence rate

In this paper, we investigate the learning-based adaptive optimal output regulation problem with convergence rate requirement for disturbed linear continuous-time systems. An adaptive optimal control approach is proposed based on reinforcement learning and adaptive dynamic programming to learn the o...

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Published in:	Control engineering practice Vol. 121; p. 105042
Main Authors:	Jiang, Yi, Gao, Weinan, Na, Jing, Zhang, Di, Hämäläinen, Timo T., Stojanovic, Vladimir, Lewis, Frank L.
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.04.2022
Subjects:	Adaptive dynamic programming Assured convergence rate Optimal output regulation Reinforcement learning Value iteration Value iteration Adaptive dynamic programming Optimal output regulation Reinforcement learning Assured convergence rate
ISSN:	0967-0661, 1873-6939
Online Access:	Get full text
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Abstract	In this paper, we investigate the learning-based adaptive optimal output regulation problem with convergence rate requirement for disturbed linear continuous-time systems. An adaptive optimal control approach is proposed based on reinforcement learning and adaptive dynamic programming to learn the optimal regulator with assured convergence rate. The above-mentioned problem is successfully solved by tackling a static optimization problem to find the optimal solution to the regulator equations, and a dynamic and constrained optimization problem to obtain the optimal feedback control gain. Without requiring on the accurate system dynamics or a stabilizing feedback control gain, a novel online value iteration algorithm is proposed, which can learn both the optimal feedback control gain and the corresponding feedforward control gain using measurable data. Moreover, the output of the closed-loop system is guaranteed to converge faster or equal to a predefined convergence rate set by user. Finally, the numerical analysis on a LCL coupled inverter-based distributed generation system shows that the proposed approach can achieve desired disturbance rejection and tracking performance.
AbstractList	In this paper, we investigate the learning-based adaptive optimal output regulation problem with convergence rate requirement for disturbed linear continuous-time systems. An adaptive optimal control approach is proposed based on reinforcement learning and adaptive dynamic programming to learn the optimal regulator with assured convergence rate. The above-mentioned problem is successfully solved by tackling a static optimization problem to find the optimal solution to the regulator equations, and a dynamic and constrained optimization problem to obtain the optimal feedback control gain. Without requiring on the accurate system dynamics or a stabilizing feedback control gain, a novel online value iteration algorithm is proposed, which can learn both the optimal feedback control gain and the corresponding feedforward control gain using measurable data. Moreover, the output of the closed-loop system is guaranteed to converge faster or equal to a predefined convergence rate set by user. Finally, the numerical analysis on a LCL coupled inverter-based distributed generation system shows that the proposed approach can achieve desired disturbance rejection and tracking performance.
ArticleNumber	105042
Author	Gao, Weinan Hämäläinen, Timo T. Jiang, Yi Na, Jing Lewis, Frank L. Stojanovic, Vladimir Zhang, Di
Author_xml	– sequence: 1 givenname: Yi orcidid: 0000-0001-8927-0119 surname: Jiang fullname: Jiang, Yi email: yjian22@cityu.edu.hk organization: Department of Biomedical Engineering, City University of Hong Kong, Hong Kong Special Administrative Region of China – sequence: 2 givenname: Weinan orcidid: 0000-0001-7921-018X surname: Gao fullname: Gao, Weinan email: wgao@fit.edu organization: Department of Mechanical and Civil Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA – sequence: 3 givenname: Jing surname: Na fullname: Na, Jing email: najing25@163.com, najing25@kust.edu.cn organization: Faculty of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming 650500, China – sequence: 4 givenname: Di surname: Zhang fullname: Zhang, Di email: d.zhang@jyu.fi organization: Faculty of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35, Jyväskylä, FIN-40014, Finland – sequence: 5 givenname: Timo T. surname: Hämäläinen fullname: Hämäläinen, Timo T. email: timo.t.hamalainen@jyu.fi organization: Faculty of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35, Jyväskylä, FIN-40014, Finland – sequence: 6 givenname: Vladimir surname: Stojanovic fullname: Stojanovic, Vladimir email: vladostojanovic@mts.rs organization: Faculty of Mechanical and Civil Engineering, University of Kragujevac, Kraljevo 36000, Serbia – sequence: 7 givenname: Frank L. surname: Lewis fullname: Lewis, Frank L. email: lewis@uta.edu organization: UTA Research Institute, the University of Texas at Arlington, Fort Worth, TX 76118, USA
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Snippet	In this paper, we investigate the learning-based adaptive optimal output regulation problem with convergence rate requirement for disturbed linear...
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SubjectTerms	Adaptive dynamic programming Assured convergence rate Optimal output regulation Reinforcement learning Value iteration
Title	Value iteration and adaptive optimal output regulation with assured convergence rate
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