Integral Reinforcement Learning-Based Online Adaptive Dynamic Event-Triggered Control Design in Mixed Zero-Sum Games for Unknown Nonlinear Systems
Mixed zero-sum games consider both zero-sum and non-zero-sum differential game problems simultaneously. In this paper, multiplayer mixed zero-sum games (MZSGs) are studied by the means of an integral reinforcement learning (IRL) algorithm under the dynamic event-triggered control (DETC) mechanism fo...
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| Format: | Article |
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MDPI AG
2024-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/24/3916 |
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| author | Yuling Liang Zhi Shao Hanguang Su Lei Liu Xiao Mao |
| author_facet | Yuling Liang Zhi Shao Hanguang Su Lei Liu Xiao Mao |
| author_sort | Yuling Liang |
| collection | DOAJ |
| description | Mixed zero-sum games consider both zero-sum and non-zero-sum differential game problems simultaneously. In this paper, multiplayer mixed zero-sum games (MZSGs) are studied by the means of an integral reinforcement learning (IRL) algorithm under the dynamic event-triggered control (DETC) mechanism for completely unknown nonlinear systems. Firstly, the adaptive dynamic programming (ADP)-based on-policy approach is proposed for solving the MZSG problem for the nonlinear system with multiple players. Secondly, to avoid using dynamic information of the system, a model-free control strategy is developed by utilizing actor–critic neural networks (NNs) for addressing the MZSG problem of unknown systems. On this basis, for the purpose of avoiding wasted communication and computing resources, the dynamic event-triggered mechanism is integrated into the integral reinforcement learning algorithm, in which a dynamic triggering condition is designed to further reduce triggering times. With the help of the Lyapunov stability theorem, the system states and weight values of NNs are proven to be uniformly ultimately bounded (UUB) stable. Finally, two examples are demonstrated to show the effectiveness and feasibility of the developed control method. Compared with static event-triggering mode, the simulation results show that the number of actuator updates in the DETC mechanism has been reduced by 55% and 69%, respectively. |
| format | Article |
| id | doaj-art-4d54ccada8da4aa4af8a8014dc4081c4 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-4d54ccada8da4aa4af8a8014dc4081c42024-12-27T14:38:00ZengMDPI AGMathematics2227-73902024-12-011224391610.3390/math12243916Integral Reinforcement Learning-Based Online Adaptive Dynamic Event-Triggered Control Design in Mixed Zero-Sum Games for Unknown Nonlinear SystemsYuling Liang0Zhi Shao1Hanguang Su2Lei Liu3Xiao Mao4School of Artificial Intelligence, Shenyang University of Technology, Shenyang 110870, ChinaSchool of Artificial Intelligence, Shenyang University of Technology, Shenyang 110870, ChinaSchool of Information Science and Engineer, Northeastern University, Shenyang 110819, ChinaSchool of Science, Liaoning University of Technology, Jinzhou 121000, ChinaSchool of Artificial Intelligence, Shenyang University of Technology, Shenyang 110870, ChinaMixed zero-sum games consider both zero-sum and non-zero-sum differential game problems simultaneously. In this paper, multiplayer mixed zero-sum games (MZSGs) are studied by the means of an integral reinforcement learning (IRL) algorithm under the dynamic event-triggered control (DETC) mechanism for completely unknown nonlinear systems. Firstly, the adaptive dynamic programming (ADP)-based on-policy approach is proposed for solving the MZSG problem for the nonlinear system with multiple players. Secondly, to avoid using dynamic information of the system, a model-free control strategy is developed by utilizing actor–critic neural networks (NNs) for addressing the MZSG problem of unknown systems. On this basis, for the purpose of avoiding wasted communication and computing resources, the dynamic event-triggered mechanism is integrated into the integral reinforcement learning algorithm, in which a dynamic triggering condition is designed to further reduce triggering times. With the help of the Lyapunov stability theorem, the system states and weight values of NNs are proven to be uniformly ultimately bounded (UUB) stable. Finally, two examples are demonstrated to show the effectiveness and feasibility of the developed control method. Compared with static event-triggering mode, the simulation results show that the number of actuator updates in the DETC mechanism has been reduced by 55% and 69%, respectively.https://www.mdpi.com/2227-7390/12/24/3916dynamic event-triggered controlintegral reinforcement learningadaptive dynamic programmingadaptive critic designmixed zero-sum games |
| spellingShingle | Yuling Liang Zhi Shao Hanguang Su Lei Liu Xiao Mao Integral Reinforcement Learning-Based Online Adaptive Dynamic Event-Triggered Control Design in Mixed Zero-Sum Games for Unknown Nonlinear Systems Mathematics dynamic event-triggered control integral reinforcement learning adaptive dynamic programming adaptive critic design mixed zero-sum games |
| title | Integral Reinforcement Learning-Based Online Adaptive Dynamic Event-Triggered Control Design in Mixed Zero-Sum Games for Unknown Nonlinear Systems |
| title_full | Integral Reinforcement Learning-Based Online Adaptive Dynamic Event-Triggered Control Design in Mixed Zero-Sum Games for Unknown Nonlinear Systems |
| title_fullStr | Integral Reinforcement Learning-Based Online Adaptive Dynamic Event-Triggered Control Design in Mixed Zero-Sum Games for Unknown Nonlinear Systems |
| title_full_unstemmed | Integral Reinforcement Learning-Based Online Adaptive Dynamic Event-Triggered Control Design in Mixed Zero-Sum Games for Unknown Nonlinear Systems |
| title_short | Integral Reinforcement Learning-Based Online Adaptive Dynamic Event-Triggered Control Design in Mixed Zero-Sum Games for Unknown Nonlinear Systems |
| title_sort | integral reinforcement learning based online adaptive dynamic event triggered control design in mixed zero sum games for unknown nonlinear systems |
| topic | dynamic event-triggered control integral reinforcement learning adaptive dynamic programming adaptive critic design mixed zero-sum games |
| url | https://www.mdpi.com/2227-7390/12/24/3916 |
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