未知非线性零和博弈最优跟踪的事件触发控制设计

王鼎; 胡凌治; 赵明明; 哈明鸣; 乔俊飞

doi:10.16383/j.aas.c220378

未知非线性零和博弈最优跟踪的事件触发控制设计

doi: 10.16383/j.aas.c220378

王鼎^{1, 2, 3, 4,},
胡凌治^{1, 2, 3, 4,},
赵明明^{1, 2, 3, 4,},
哈明鸣^5,,
乔俊飞^{1, 2, 3, 4,}

1.
北京工业大学信息学部北京 100124
2.
计算智能与智能系统北京市重点实验室北京 100124
3.
北京人工智能研究院北京 100124
4.
智慧环保北京实验室北京 100124
5.
北京科技大学自动化与电气工程学院北京 100083

基金项目: 科技创新2030—“新一代人工智能”重大项目(2021ZD0112302), 北京市自然科学基金(JQ19013), 国家自然科学基金(62222301, 61890930-5, 62021003)资助

详细信息

作者简介:
王鼎：北京工业大学信息学部教授. 2009年获得东北大学硕士学位, 2012年获得中国科学院自动化研究所博士学位. 主要研究方向为强化学习与智能控制. 本文通信作者. E-mail: dingwang@bjut.edu.cn

胡凌治：北京工业大学信息学部硕士研究生. 主要研究方向为强化学习和智能控制. E-mail: hulingzhi@email s.bjut.edu.cn

赵明明：北京工业大学信息学部博士研究生. 主要研究方向为强化学习和智能控制. E-mail: zhaomm@emails.bjut.edu.cn

哈明鸣：北京科技大学自动化与电气工程学院博士研究生. 分别于2016年和2019年获得北京科技大学学士和硕士学位. 主要研究方向为最优控制, 自适应动态规划和强化学习. E-mail: hamingming_0705@foxmail.com

乔俊飞：北京工业大学信息学部教授. 主要研究方向为污水处理过程智能控制和神经网络结构设计与优化. E-mail: adqiao@bjut.edu.cn

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出版历程
- 收稿日期: 2022-05-09
- 录用日期: 2022-07-13
- 网络出版日期: 2022-08-05
- 刊出日期: 2023-01-07

Event-triggered Control Design for Optimal Tracking of Unknown Nonlinear Zero-sum Games

WANG Ding^{1, 2, 3, 4
,},
HU Ling-Zhi^{1, 2, 3, 4
,},
ZHAO Ming-Ming^{1, 2, 3, 4
,},
HA Ming-Ming^5
,,
QIAO Jun-Fei^{1, 2, 3, 4
,}

1.
Faculty of Information Technology, Beijing University of Technology, Beijing 100124
2.
Beijing Key Laboratory of Computational Intelligence and Intelligent System, Beijing 100124
3.
Beijing Institute of Artificial Intelligence, Beijing 100124
4.
Beijing Laboratory of Smart Environmental Protection, Beijing 100124
5.
School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083

Funds: Supported by National Key Research and Development Program of China (2021ZD0112302), Beijing Natural Science Foundation (JQ19013), and National Natural Science Foundation of China (62222301, 61890930-5, 62021003)

More Information

Author Bio:
WANG Ding　Professor at the Faculty of Information Technology, Beijing University of Technology. He received his master degree from Northeastern University in 2009 and received his Ph.D. degree from Institute of Automation, Chinese Academy of Sciences in 2012. His research interest covers reinforcement learning and intelligent control. Corresponding author of this paper

HU Ling-Zhi　Master student at the Faculty of Information Technology, Beijing University of Technology. His research interest covers reinforcement learning and intelligent control

ZHAO Ming-Ming　Ph.D. candidate at the Faculty of Information Technology, Beijing University of Technology. His research interest covers reinforcement learning and intelligent control

HA Ming-Ming　Ph.D. candidate at the School of Automation and Electrical Engineering, University of Science and Technology Beijing. He received his bachelor and master degrees from University of Science and Technology Beijing in 2016 and 2019, respectively. His research interest covers optimal control, adaptive dynamic programming, and reinforcement learning

QIAO Jun-Fei　Professor at the Faculty of Information Technology, Beijing University of Technology. His research interest covers intelligent control of wastewater treatment processes, structure design and optimization of neural networks

摘要

摘要: 设计了一种基于事件的迭代自适应评判算法, 用于解决一类非仿射系统的零和博弈最优跟踪控制问题. 通过数值求解方法得到参考轨迹的稳定控制, 进而将未知非线性系统的零和博弈最优跟踪控制问题转化为误差系统的最优调节问题. 为了保证闭环系统在具有良好控制性能的基础上有效地提高资源利用率, 引入一个合适的事件触发条件来获得阶段性更新的跟踪策略对. 然后, 根据设计的触发条件, 采用Lyapunov方法证明误差系统的渐近稳定性. 接着, 通过构建四个神经网络, 来促进所提算法的实现. 为了提高目标轨迹对应稳定控制的精度, 采用模型网络直接逼近未知系统函数而不是误差动态系统. 构建评判网络、执行网络和扰动网络用于近似迭代代价函数和迭代跟踪策略对. 最后, 通过两个仿真实例, 验证该控制方法的可行性和有效性.
- 自适应评判设计 /
- 事件触发控制 /
- 神经网络 /
- 最优跟踪控制 /
- 稳定性分析 /
- 零和博弈
Abstract: In this paper, an event-based iterative adaptive critic algorithm is designed to address optimal tracking control for a class of nonaffine zero-sum games. The steady control of the reference trajectory is obtained by numerical calculation. Then, the optimal tracking control problem of unknown nonlinear zero-sum games is transformed into the optimal regulation problem of corresponding error dynamics. In order to ensure that the closed-loop system possesses favourable control performance while can effectively improve the resource utilization, an appropriate event-triggering condition is introduced to obtain the tracking policy pair aperiodically. According to the designed triggering condition and the Lyapunov stability theory, the error system is proved to be asymptotically stable. In addition, four neural networks are constructed to promote the implementation of the proposed algorithm. In order to improve the accuracy of the steady control in target trajectory, the model network is used to approach the unknown system function directly instead of the error dynamic system. The critic network, the action network, and the disturbance network are constructed to obtain the approximate iterative cost function and the approximate iterative tracking policy pair. Finally, two examples are presented to demonstrate the feasibility and effectiveness of the proposed algorithm.
- Adaptive critic design /
- event-triggered control /
- neural networks /
- optimal tracking control /
- stability analysis /
- zero-sum games

HTML全文

图 1 基于事件的零和博弈跟踪控制方法示意图

Fig. 1 The simple structure of the event-based zero-sum game tracking control method

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图 2 模型网络训练误差 (例1)

Fig. 2 The training errors of the model network(Example 1)

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图 3 系统状态、控制律和扰动律轨迹(例1)

Fig. 3 Trajectories of the state, the control law, and the disturbance law (Example 1)

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图 4 跟踪误差、跟踪控制律和跟踪扰动律轨迹(例1)

Fig. 4 Trajectories of the tracking error, the tracking control law, and the tracking disturbance law (Example 1)

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图 5 稳定控制$ v(\xi_k) $(例1)

Fig. 5 The steady control $ v(\xi_k) $ (Example 1)

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图 6 触发阈值$ \sigma_T $(例1)

Fig. 6 The triggering threshold $ \sigma_T $ (Example 1)

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图 7 模型网络训练误差(例2)

Fig. 7 The training errors of the model network(Example 2)

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图 8 系统状态、控制律和扰动律轨迹(例2)

Fig. 8 Trajectories of the state, the control law, and the disturbance law (Example 2)

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图 9 跟踪误差、跟踪控制律和跟踪扰动律轨迹(例2)

Fig. 9 Trajectories of the tracking error, the tracking control law, and the tracking disturbance law (Example 2)

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图 10 触发阈值$ \sigma_T $(例2)

Fig. 10 The triggering threshold $ \sigma_T $ (Example 2)

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表 1 两个仿真实验的主要参数

Table 1 Main parameters of two experimental examples

符号	例 1	例 2
$ {\cal{Q}} $	$ 0.01I_2 $	$ 0.1I_2 $
$ {\cal{R}} $	$ I $	$ I $
$ \gamma $	$ 0.01 $	$ 0.1 $
$ \Gamma $	$ 0.2 $	$ 0.35 $
$ \beta $	$ 1/6 $	$ 7/27 $
$ \epsilon $	$ 10^{-5} $	$ 10^{-5} $

下载: 导出CSV

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