A reinforcement learning methodology to hierarchical sliding‐mode surface H∞ control of nonlinear systems via a dynamic event‐triggered mechanism

Summary This paper addresses the problem of a hierarchical sliding mode surface (HSMS) H∞$$ {H}_{\infty } $$ control design for nonlinear systems via a dynamic event‐triggered mechanism. Initially, the HSMS containing the system states is constructed to enhance the system's response rate and ro...

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Bibliographic Details
Published in:Asian journal of control Vol. 27; no. 5; pp. 2224 - 2242
Main Authors: Wang, Tengda, Karimi, Hamid Reza, Wang, Huanqing, Xu, Ning, Li, Lun, Zhao, Xudong
Format: Journal Article
Language:English
Published: Hoboken Wiley Subscription Services, Inc 01.09.2025
Subjects:
Control methods
Control systems
Cost function
dynamic event‐triggered mechanism
H-infinity control
hierarchical sliding‐mode surface technique
H∞$$ {H}_{\infty } $$ control
Machine learning
neural network
Nonlinear control
Nonlinear systems
reinforcement learning
Tunnel diodes
Zero sum games
ISSN:1561-8625, 1934-6093
Online Access:Get full text
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Summary:Summary This paper addresses the problem of a hierarchical sliding mode surface (HSMS) H∞$$ {H}_{\infty } $$ control design for nonlinear systems via a dynamic event‐triggered mechanism. Initially, the HSMS containing the system states is constructed to enhance the system's response rate and robustness. By assigning a cost function associated with the HSMS, such an H∞$$ {H}_{\infty } $$ control problem is equivalently transformed into a zero‐sum game problem, where the control policy and the exogenous disturbance are treated as two players with opposite interests. Afterwards, a novel dynamic event‐triggered mechanism is designed, where the triggering condition depends on HSMS variables. To solve the corresponding event‐triggered Hamilton–Jacobi–Isaacs equation, a single‐critic reinforcement learning algorithm is developed, which removes the error generated by approximating the actor network in the actor‐critic network. According to the Lyapunov stability theory, all signals of the considered system are strictly proved to be bounded. Finally, the validity of the proposed control method is demonstrated through simulations of a tunnel diode circuit system and a mass‐spring‐damper system.
Bibliography:Preprint submitted to Asian J Control.
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ISSN:1561-8625
1934-6093
DOI:10.1002/asjc.3569