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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| Vydáno v: | Asian journal of control Ročník 27; číslo 5; s. 2224 - 2242 |
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| Hlavní autoři: | , , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Hoboken
Wiley Subscription Services, Inc
01.09.2025
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| ISSN: | 1561-8625, 1934-6093 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. This paper addresses the problem of a hierarchical sliding mode surface (HSMS) 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 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. 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. |
| Author | Wang, Huanqing Xu, Ning Karimi, Hamid Reza Zhao, Xudong Wang, Tengda Li, Lun |
| Author_xml | – sequence: 1 givenname: Tengda orcidid: 0000-0001-9462-9341 surname: Wang fullname: Wang, Tengda organization: Bohai University – sequence: 2 givenname: Hamid Reza orcidid: 0000-0001-7629-3266 surname: Karimi fullname: Karimi, Hamid Reza organization: Politecnico di Milano – sequence: 3 givenname: Huanqing orcidid: 0000-0001-5712-9356 surname: Wang fullname: Wang, Huanqing organization: Bohai University – sequence: 4 givenname: Ning orcidid: 0000-0002-0717-1713 surname: Xu fullname: Xu, Ning organization: Bohai University – sequence: 5 givenname: Lun surname: Li fullname: Li, Lun organization: Weifang University – sequence: 6 givenname: Xudong orcidid: 0000-0002-1864-4686 surname: Zhao fullname: Zhao, Xudong email: xdzhaohit@gmail.com organization: Dalian University of Technology |
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This paper addresses the problem of a hierarchical sliding mode surface (HSMS)
H∞$$ {H}_{\infty } $$ control design for nonlinear systems via a dynamic... This paper addresses the problem of a hierarchical sliding mode surface (HSMS) control design for nonlinear systems via a dynamic event‐triggered mechanism.... This paper addresses the problem of a hierarchical sliding mode surface (HSMS) H∞$$ {H}_{\infty } $$ control design for nonlinear systems via a dynamic... |
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| SubjectTerms | 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 |
| Title | A reinforcement learning methodology to hierarchical sliding‐mode surface H∞ control of nonlinear systems via a dynamic event‐triggered mechanism |
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