非线性离散时间系统最优切换解耦控制方法

王香智; 富月

doi:10.16383/j.aas.c260022

非线性离散时间系统最优切换解耦控制方法

doi: 10.16383/j.aas.c260022 cstr: 32138.14.j.aas.c260022

王香智^1,,
富月^1,

1.
东北大学流程工业综合自动化全国重点实验室沈阳 110819

基金项目: 国家自然科学基金(62573105, 62333004, 61991403), 国家重点研发计划(2024YFA1012700)资助

详细信息

作者简介:
王香智：东北大学流程工业综合自动化全国重点实验室硕士研究生. 2022年获得沈阳工业大学学士学位. 主要研究方向为近似最优控制和自适应控制.E-mail: wangxiangzhi_neu@163.com

富月：东北大学流程工业综合自动化全国重点实验室教授. 2009年获得东北大学控制理论与控制工程专业博士学位. 主要研究方向为复杂工业过程自适应控制, 智能解耦控制, 近似动态规划和工业过程运行控制. 本文通信作者. E-mail: fuyue@mail.neu.edu.cn

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出版历程
- 收稿日期: 2026-01-09
- 录用日期: 2026-05-13
- 网络出版日期: 2026-09-14

Nonlinear Discrete-time System Optimal Switching Decoupling Control

WANG Xiang-Zhi^1
,,
FU Yue^1
,

1.
State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819

Funds: Supported by National Natural Science Foundation of China (62573105, 62333004, 61991403) and National Key R&D Program of China (2024YFA1012700)

More Information

Author Bio:
WANG Xiang-Zhi　Master student at the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. He received his bachelor degree from Shenyang University of Technology in 2022. His research interests include approximate optimal control and adaptive control

FU Yue　Professor at the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. She received her Ph.D. degree in control theory and control engineering from Northeastern University in 2009. Her research interests include adaptive control of complex industrial processes, intelligent decoupling control, approximate dynamic programming, and operational control of industrial processes. Corresponding author of this paper

摘要

摘要: 针对具有多个运行点的非线性离散时间多变量强耦合系统, 提出一种最优切换解耦控制方法. 首先, 将非线性系统在多个运行点附近泰勒展开, 得到多个近似线性模型, 通过引入开关函数, 并利用矩阵分解方法建立控制器设计模型; 然后, 基于考虑耦合影响的复合型性能指标, 利用嵌入转换技术、极小值原理及二次规划技术, 推导出最优切换准则函数及最优切换解耦控制器, 并设计鲁棒补偿器以提升控制系统性能; 最后, 进行数值仿真实验, 实验结果验证了所提方法的有效性及优越性.
- 最优跟踪控制 /
- 解耦 /
- 切换控制 /
- 多变量强耦合系统 /
- 离散时间非线性系统
Abstract: An optimal switching decoupling control method is proposed for nonlinear discrete-time multivariable systems with multiple operating points and strong coupling. First, the nonlinear system is approximated by several local linear models obtained via Taylor expansion around multiple operating points. A switching function is introduced, and a controller design model is established using matrix decomposition techniques. Then, based on a composite performance index that takes coupling effects into account, the optimal switching criterion function and the optimal switching decoupled controller are derived using embedding transformation technique, the minimum principle, and quadratic programming technique. A robust compensator is further designed to enhance the performance of the control system. Finally, numerical simulations are conducted, and the results verify the effectiveness and superiority of the proposed method.
- optimal tracking control /
- decoupling /
- switching control /
- strongly coupled multivariable systems /
- discrete-time nonlinear systems

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图 1 具有鲁棒特性的最优切换解耦控制系统结构

Fig. 1 Structure of the robust optimal switching decoupling control system

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图 2 采用本文所提方法时系统的液位

Fig. 2 Liquid levels of the system using the method proposed in this paper

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图 4 采用本文所提方法时系统的切换序列

Fig. 4 Switching sequence of the system using the method proposed in this paper

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图 5 采用文献[22]所提方法时系统的液位

Fig. 5 Liquid levels of the system using the method proposed in reference [22]

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图 6 采用文献[22]所提方法时系统的控制输入

Fig. 6 Control inputs of the system using the method proposed in reference [22]

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图 3 采用本文所提方法时系统的控制输入

Fig. 3 Control inputs of the system using the method proposed in this paper

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图 7 两种方法的评估函数曲线

Fig. 7 Evaluation function curves of the two methods

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表 1 两种方法的RMSE

Table 1 RMSE of two methods

控制算法 RMSE

文献[22]所提方法 $0.442\;0$

本文所提方法 $0.277\;8\;(\downarrow 37.1\%)$

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