融合自适应评判的随机系统数据驱动策略优化

王鼎; 王将宇; 乔俊飞

doi:10.16383/j.aas.c230678

融合自适应评判的随机系统数据驱动策略优化

doi: 10.16383/j.aas.c230678

王鼎^{1, 2, 3, 4,},
王将宇^{1, 2, 3, 4,},
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

基金项目: 国家自然科学基金 (62222301, 61890930-5, 62021003), 科技创新2030 ——“新一代人工智能”重大项目 (2021ZD0112302, 2021ZD0112301) 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

王将宇：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: wangjiangyu@emails.bjut.edu.cn

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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- 被引次数: 0
出版历程
- 收稿日期: 2023-11-02
- 录用日期: 2024-01-08
- 网络出版日期: 2024-02-19
- 刊出日期: 2024-05-29

Data-driven Policy Optimization for Stochastic Systems Involving Adaptive Critic

WANG Ding^{1, 2, 3, 4
,},
WANG Jiang-Yu^{1, 2, 3, 4
,},
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

Funds: Supported by National Natural Science Foundation of China (62222301, 61890930-5, 62021003) and National Key Research and Development Program of China (2021ZD0112302, 2021ZD0112301)

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 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

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

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: 自适应评判技术已经广泛应用于求解复杂非线性系统的最优控制问题, 但利用其求解离散时间非线性随机系统的无限时域最优控制问题还存在一定局限性. 本文融合自适应评判技术, 建立一种数据驱动的离散随机系统折扣最优调节方法. 首先, 针对宽松假设下的非线性随机系统, 研究带有折扣因子的无限时域最优控制问题. 所提的随机系统 Q-learning 算法能够将初始的容许策略单调不增地优化至最优策略. 基于数据驱动思想, 随机系统 Q-learning 算法在不建立模型的情况下直接利用数据进行策略优化. 其次, 利用执行−评判神经网络方案, 实现了随机系统 Q-learning 算法. 最后, 通过两个基准系统, 验证本文提出的随机系统 Q-learning 算法的有效性.
- 自适应评判设计 /
- 数据驱动 /
- 离散系统 /
- 神经网络 /
- Q-learning /
- 随机最优控制
Abstract: Adaptive critic technology has been widely employed to solve the optimal control problems of complicated nonlinear systems, but there are some limitations to solve the infinite-horizon optimal problems of discrete-time nonlinear stochastic systems. In this paper, we establish a data-driven discounted optimal regulation method for discrete-time stochastic systems involving adaptive critic technology. First, we investigate the infinite-horizon optimal problems with the discount factor for stochastic systems under the relaxed assumption. The developed stochastic Q-learning algorithm can optimize an initial admissible policy to the optimal one in a monotonically nonincreasing way. Based on the data-driven idea, the policy optimization of the stochastic Q-learning algorithm is executed without a dynamic model. Then, the stochastic Q-learning algorithm is implemented by utilizing the actor-critic neural networks. Finally, two nonlinear benchmarks are given to demonstrate the overall performance of the developed stochastic Q-learning algorithm.
- Adaptive critic design /
- data-driven /
- discrete-time systems /
- neural networks /
- Q-learning /
- stochastic optimal control

HTML全文

图 1 Q 网络权值曲线 (基准系统 I)

Fig. 1 Curves of Q network weights (Benchmark system I)

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图 2 执行网络权值曲线 (基准系统 I)

Fig. 2 Curves of action network weights (Benchmark system I)

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图 3 控制策略测试曲线 (基准系统 I)

Fig. 3 Curves of control policies for performance test (Benchmark system I)

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图 4 球台平衡系统示意图 (基准系统II)

Fig. 4 Schematic diagram of the ball-and-beam system (Benchmark system II)

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图 5 Q 网络权值曲线 (基准系统II)

Fig. 5 Curves of Q network weights (Benchmark system II)

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图 6 执行网络权值曲线 (基准系统 II)

Fig. 6 Curves of action network weights (Benchmark system II)

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图 7 系统状态曲线 (基准系统 II)

Fig. 7 Curves of system states (Benchmark system II)

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图 8 系统控制输入曲线 (基准系统 II)

Fig. 8 Curves of system control inputs (Benchmark system II)

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图 9 代价函数曲线 (基准系统 II)

Fig. 9 Curves of cost-to-go (Benchmark system II)

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表 1 随机 Q-learning 算法的主要参数

Table 1 Main parameters of the stochastic Q-learning algorithm

算法参数	$\mathcal{Q}$	$\mathcal{R}$	${\rho}_{\max}$	$\lambda$	$\epsilon$
基准系统I	$2I_2$	2.0	300	0.97	0.01
基准系统II	$0.1I_4$	0.1	500	0.99	0.01

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表 2 球台平衡系统的主要参数

Table 2 Main parameters of the ball-and-beam system

符号及取值	物理意义
$S_t=0.001 \;{\rm{N}}/ {\rm{m}}$	驱动机械刚度
$L_\omega =0.5\; {\rm{m}}$	平台半径
$L =0.48 \; {\rm{m}}$	电机作用半径
$f_c= 1\; {\rm{N_s/ m}}$	驱动电机的机械摩擦系数
$I_\omega = 0.140\;25 \;{\rm{kg} }\cdot {\rm{m} }^2$	平台惯性矩
$g = 9.8\; {\rm{m/s}}^2$	重力加速度
$\varpi =0.016\;2 \;{\rm{kg} }$	球体质量
$\tau =0.02 \;{\rm{m}}$	球体滚动半径
$I_b=4.32\times10^{-5} \;{\rm{kg}}\cdot {\rm{m}}^2$	球体转动惯量

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