H∞ optimal control of unknown linear systems by adaptive dynamic programming with applications to time‐delay systems

In this paper, a new value iteration (VI) based method is proposed to solve the H∞ control problem of continuous‐time linear systems. The problem is transformed into solving a nonlinear differential equation, and the local stability of its solution is proved. Then a VI based iteration scheme for get...

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Bibliographic Details
Published in:International journal of robust and nonlinear control Vol. 31; no. 12; pp. 5602 - 5617
Main Authors: Jiang, Huai‐Yuan, Zhou, Bin, Liu, Guo‐Ping
Format: Journal Article
Language:English
Published: Bognor Regis Wiley Subscription Services, Inc 01.08.2021
Subjects:
adaptive dynamic programming
Adaptive systems
Attenuation
Dynamic programming
H-infinity control
linear H∞ control
Linear systems
model free control
Nonlinear differential equations
Optimal control
System effectiveness
time‐delay systems
zero‐sum differential games
ISSN:1049-8923, 1099-1239
Online Access:Get full text
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Summary:In this paper, a new value iteration (VI) based method is proposed to solve the H∞ control problem of continuous‐time linear systems. The problem is transformed into solving a nonlinear differential equation, and the local stability of its solution is proved. Then a VI based iteration scheme for getting the approximation of the H∞ optimal controller is proposed. Compared with the existing results, the proposed scheme does not need any special initial matrix or extra condition to solve the problem and provides a relatively small disturbance attenuation bound. The related result is also applied to the quadratic guaranteed cost control of linear time‐delay systems. Simulation examples verify the effectiveness of the proposed schemes.
Bibliography:Funding information
National Natural Science Foundation of China, 61773140; 61690212
ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.5557