Application of an Off‐Policy Reinforcement Learning Algorithm for H∞${{H}_\infty }$ Control Design of Nonlinear Structural Systems With Completely Unknown Dynamics
ABSTRACT This paper proposes a model‐free and online off‐policy algorithm based on reinforcement learning (RL) for vibration attenuation of earthquake‐excited structures, through designing an optimal H∞${{H}_\infty }$ controller. This design relies on solving a two‐player zero‐sum game theory with a...
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| Published in: | Earthquake engineering & structural dynamics Vol. 54; no. 4; pp. 1210 - 1228 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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01.04.2025
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| ISSN: | 0098-8847, 1096-9845 |
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| Abstract | ABSTRACT
This paper proposes a model‐free and online off‐policy algorithm based on reinforcement learning (RL) for vibration attenuation of earthquake‐excited structures, through designing an optimal H∞${{H}_\infty }$ controller. This design relies on solving a two‐player zero‐sum game theory with a Hamilton–Jacobi–Isaacs (HJI) equation, which is extremely difficult, or often impossible, to be solved for the value function and the related optimal controller. The proposed strategy uses an actor‐critic‐disturbance structure to learn the solution of the HJI equation online and forward in time, without requiring any knowledge of the system dynamics. In addition, the control and disturbance policies and value function are approximated by the actor, the disturbance, and the critic neural networks (NNs), respectively.
Implementing the policy iteration technique, the NNs’ weights of the proposed model are calculated using the least square (LS) method in each iteration. In the present study, the convergence of the proposed algorithm is investigated through two distinct examples. Furthermore, the performance of this off‐policy RL strategy is studied in reducing the response of a seismically excited nonlinear structure with an active mass damper (AMD) for two cases of state feedback. The simulation results prove the effectiveness of the proposed algorithm in application to civil engineering structures. |
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| AbstractList | This paper proposes a model‐free and online off‐policy algorithm based on reinforcement learning (RL) for vibration attenuation of earthquake‐excited structures, through designing an optimal controller. This design relies on solving a two‐player zero‐sum game theory with a Hamilton–Jacobi–Isaacs (HJI) equation, which is extremely difficult, or often impossible, to be solved for the value function and the related optimal controller. The proposed strategy uses an actor‐critic‐disturbance structure to learn the solution of the HJI equation online and forward in time, without requiring any knowledge of the system dynamics. In addition, the control and disturbance policies and value function are approximated by the actor, the disturbance, and the critic neural networks (NNs), respectively.
Implementing the policy iteration technique, the NNs’ weights of the proposed model are calculated using the least square (LS) method in each iteration. In the present study, the convergence of the proposed algorithm is investigated through two distinct examples. Furthermore, the performance of this off‐policy RL strategy is studied in reducing the response of a seismically excited nonlinear structure with an active mass damper (AMD) for two cases of state feedback. The simulation results prove the effectiveness of the proposed algorithm in application to civil engineering structures. ABSTRACT This paper proposes a model‐free and online off‐policy algorithm based on reinforcement learning (RL) for vibration attenuation of earthquake‐excited structures, through designing an optimal H∞${{H}_\infty }$ controller. This design relies on solving a two‐player zero‐sum game theory with a Hamilton–Jacobi–Isaacs (HJI) equation, which is extremely difficult, or often impossible, to be solved for the value function and the related optimal controller. The proposed strategy uses an actor‐critic‐disturbance structure to learn the solution of the HJI equation online and forward in time, without requiring any knowledge of the system dynamics. In addition, the control and disturbance policies and value function are approximated by the actor, the disturbance, and the critic neural networks (NNs), respectively. Implementing the policy iteration technique, the NNs’ weights of the proposed model are calculated using the least square (LS) method in each iteration. In the present study, the convergence of the proposed algorithm is investigated through two distinct examples. Furthermore, the performance of this off‐policy RL strategy is studied in reducing the response of a seismically excited nonlinear structure with an active mass damper (AMD) for two cases of state feedback. The simulation results prove the effectiveness of the proposed algorithm in application to civil engineering structures. This paper proposes a model‐free and online off‐policy algorithm based on reinforcement learning (RL) for vibration attenuation of earthquake‐excited structures, through designing an optimal H∞${{H}_\infty }$ controller. This design relies on solving a two‐player zero‐sum game theory with a Hamilton–Jacobi–Isaacs (HJI) equation, which is extremely difficult, or often impossible, to be solved for the value function and the related optimal controller. The proposed strategy uses an actor‐critic‐disturbance structure to learn the solution of the HJI equation online and forward in time, without requiring any knowledge of the system dynamics. In addition, the control and disturbance policies and value function are approximated by the actor, the disturbance, and the critic neural networks (NNs), respectively.Implementing the policy iteration technique, the NNs’ weights of the proposed model are calculated using the least square (LS) method in each iteration. In the present study, the convergence of the proposed algorithm is investigated through two distinct examples. Furthermore, the performance of this off‐policy RL strategy is studied in reducing the response of a seismically excited nonlinear structure with an active mass damper (AMD) for two cases of state feedback. The simulation results prove the effectiveness of the proposed algorithm in application to civil engineering structures. |
| Author | Mojoodi, A. Shojaee, Saeed Hamzehei‐Javaran, Saleh Amirmojahedi, M. |
| Author_xml | – sequence: 1 givenname: M. surname: Amirmojahedi fullname: Amirmojahedi, M. organization: Shahid Bahonar University of Kerman – sequence: 2 givenname: A. surname: Mojoodi fullname: Mojoodi, A. organization: Amirkabir University of Technology – sequence: 3 givenname: Saeed orcidid: 0000-0003-0952-9085 surname: Shojaee fullname: Shojaee, Saeed email: saeed.shojaee@uk.ac.ir organization: Shahid Bahonar University of Kerman – sequence: 4 givenname: Saleh surname: Hamzehei‐Javaran fullname: Hamzehei‐Javaran, Saleh organization: Shahid Bahonar University of Kerman |
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| Cites_doi | 10.1002/stc.2298 10.1002/eqe.862 10.3390/app9204443 10.1109/TASE.2014.2300532 10.1002/eqe.1167 10.1007/978-3-030-60990-0 10.1109/TCYB.2014.2319577 10.1016/j.engstruct.2023.116738 10.1109/TAC.2008.2006108 10.1109/MCS.2012.2214134 10.1016/j.isatra.2023.04.009 10.1016/j.automatica.2012.06.096 10.1016/j.engstruct.2021.112819 10.1016/j.automatica.2004.11.034 10.1016/j.automatica.2011.03.005 10.1002/eqe.3432 10.1109/TNN.2008.2000204 10.1109/CDC.2010.5717607 10.1109/MED.2009.5164743 10.1007/3-540-76074-1 10.1061/(ASCE)0733‐9399(1992)118:11(2227) 10.1162/0899766053011528 10.1007/978-0-8176-4757-5 10.1109/TNNLS.2013.2294968 10.1007/s11431‐022‐2228‐0 10.1007/s11768‐011‐0166‐4 10.1061/JMCEA3.0002768 10.1002/acs.2348 10.1002/RNC.4590040409 10.1016/j.engstruct.2022.115122 10.1016/j.aei.2019.100986 10.1109/TNNLS.2015.2441749 10.1109/IJCNN.2009.5178586 10.1109/TSMC.1979.4310171 10.1002/acs.2485 10.1016/S0005‐1098(97)00128‐3 10.1080/002071798221542 |
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This paper proposes a model‐free and online off‐policy algorithm based on reinforcement learning (RL) for vibration attenuation of earthquake‐excited... This paper proposes a model‐free and online off‐policy algorithm based on reinforcement learning (RL) for vibration attenuation of earthquake‐excited... |
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| SubjectTerms | Active damping Algorithms Civil engineering Control systems design Controllers Earthquakes Game theory H-infinity control H∞${{H}_\infty }$ control Machine learning Neural networks nonlinear building Nonlinear control Nonlinear systems online reinforcement learning Policies State feedback Strategy System dynamics two‐player zero‐sum game Vibration Zero sum games |
| Title | Application of an Off‐Policy Reinforcement Learning Algorithm for H∞${{H}_\infty }$ Control Design of Nonlinear Structural Systems With Completely Unknown Dynamics |
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