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 2021-08, Vol.31 (12), p.5602-5617
Main Authors: Jiang, Huai‐Yuan, Zhou, Bin, Liu, Guo‐Ping
Format: Article
Language:English
Subjects:
Adaptive control
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
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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.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.5557