基于强化学习的部分线性离散时间系统的最优输出调节

庞文砚; 范家璐; 姜艺; LEWIS Frank Leroy

doi:10.16383/j.aas.c190853

基于强化学习的部分线性离散时间系统的最优输出调节

doi: 10.16383/j.aas.c190853

1.
东北大学流程工业综合自动化国家重点实验室沈阳 110819 中国
2.
德克萨斯大学阿灵顿分校沃斯堡 76118 美国

基金项目: 国家自然科学基金(61533015, 61991404, 61991403)和辽宁省兴辽英才计划(XLYC2007135)资助

详细信息

作者简介:
庞文砚：东北大学流程工业综合自动化国家重点实验室硕士研究生. 主要研究方向为工业过程运行控制和强化学习. E-mail: pangwy799@163.com

范家璐：东北大学流程工业综合自动化国家重点实验室副教授. 2011年获浙江大学博士学位. 主要研究方向为工业过程运行控制, 工业无线传感器网络与强化学习. 本文通信作者. E-mail: jlfan@mail.neu.edu.cn

姜艺：中国香港城市大学博士后. 2020年获东北大学控制理论与控制工程专业博士学位. 主要研究方向为工业过程运行控制, 网络控制, 自适应动态规划和强化学习. E-mail: yjian22@cityu.edu.hk

LEWIS Frank Leroy：德克萨斯大学阿灵顿分校教授. 主要研究方向为反馈控制, 强化学习, 智能系统, 协同控制系统和非线性系统. E-mail: lewis@uta.edu

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出版历程
- 收稿日期: 2019-12-16
- 录用日期: 2020-04-07
- 网络出版日期: 2021-01-20
- 刊出日期: 2022-09-16

Optimal Output Regulation of Partially Linear Discrete-time Systems Using Reinforcement Learning

1.
State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China
2.
University of Texas at Arlington, Fort Worth 76118, USA

Funds: Supported by National Natural Science Foundations of China (61533015, 61991404, 61991403) and Liaoning Revitalization Talents Program (XLYC2007135)

More Information

Author Bio:
PANG Wen-Yan　Master student at the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. Her research interest covers industrial process operational control and reinforcement learning

FAN Jia-Lu　Associate professor at the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. She received her Ph.D. degree from Zhejiang University in 2011. Her research interest covers industrial process operational control, industrial wireless sensor networks and reinforcement learning. Corresponding author of this paper

JIANG Yi　Postdoctor at City University of Hong Kong, China. He received his Ph.D. degree in control theory and engineering from Northeastern University in 2020. His research interest covers industrial process operational control, networked control, adaptive dynamic programming and reinforcement learning

LEWIS Frank Leroy　Professor at University of Texas at Arlington. His research interest covers feedback control, reinforcement learning, intelligent systems, cooperative control systems and nonlinear systems

摘要

摘要: 针对同时具有线性外部干扰与非线性不确定性下的离散时间部分线性系统的最优输出调节问题, 提出了仅利用在线数据的基于强化学习的数据驱动控制方法. 首先, 该问题可拆分为一个受约束的静态优化问题和一个动态规划问题, 第一个问题可以解出调节器方程的解. 第二个问题可以确定出控制器的最优反馈增益. 然后, 运用小增益定理证明了存在非线性不确定性离散时间部分线性系统的最优输出调节问题的稳定性. 针对传统的控制方法需要准确的系统模型参数用来解决这两个优化问题, 提出了一种数据驱动离线策略更新算法, 该算法仅使用在线数据找到动态规划问题的解. 然后, 基于动态规划问题的解, 利用在线数据为静态优化问题提供了最优解. 最后, 仿真结果验证了该方法的有效性.
- 输出调节 /
- 离散时间系统 /
- 强化学习 /
- 非线性未知动态
Abstract: A data-driven control method only using online data based on reinforcement learning is proposed for the optimal output regulation problem of discrete-time partially linear systems with both linear disturbance and nonlinear uncertainties. First, the problem can be split into a constrained static optimization problem and a dynamic one. The solution of the first problem is corresponding to the solution of the regulator equation. The second can determine the optimal feedback gain of the controller. Then the small-gain theorem is used to prove the stability of the optimal output regulation problem of discrete-time partially linear systems with nonlinear uncertainties. The traditional control method needs the dynamics of the system to solve the two problems. But for this problem, a data-driven off-policy algorithm is proposed using only the measured data to find the solution of the dynamic optimization problem. Then, based on the solution of the dynamic one, the solution of the static optimization problem can be found only using data online. Finally, simulation results verify the effectiveness of the proposed method.
- Output regulation /
- discrete-time system /
- reinforcement learning /
- nonlinear unknown dynamics

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图 1 系统输出与参考轨迹及跟踪误差

Fig. 1 Trajectories of system output and reference and tracking error

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图 3 系统干扰

Fig. 3 The disturbance of system

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图 4 学习阶段$P$和$K $的收敛情况

Fig. 4 The convergence of $P,K$ during learning phase

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图 5 误差系统状态轨迹

Fig. 5 The error system state trajectory

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图 2 控制输入轨迹

Fig. 2 The control input trajectory

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图 7 对比实验2仿真结果图

Fig. 7 The result of comparison experiment 2

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图 6 对比实验1仿真结果图

Fig. 6 The result of comparison experiment 1

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表 1 对比实验评价指标

Table 1 Performance index of comparison experiment

$220<k<280$ IAE RMSE

本文方法 1.8330×10⁻⁶ 3.6653×10⁻⁸

对比方法 8.2293 0.1349

下载: 导出CSV

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