多变量预测控制结构分解的图论方法  

Graph theory method for multivariate predictive control structure decomposition

作　　者：王洪瑞 邹涛 张鑫[1,2] 王美聪[5] 陆云松 WANG Hong-rui;ZOU Tao;ZHANG Xin;WANG Mei-cong;LU Yun-song(Shenyang Institute of Automation,Chinese Academy of Sciences,Shenyang Liaoning 110016,China;Institutes for Robotics and Intelligent Manufacturing,Chinese Academy of Sciences,Shenyang Liaoning 110016,China;University of Chinese Academy of Sciences,Beijing 100049,China;College of Mechanical and Electrical Engineering,Guangzhou University,Guangzhou Guangdong 510006,China;College of Environment and Safety Engineering,Shenyang University of Chemical Technology,Shenyang Liaoning 110142,China)

机构地区：[1]中国科学院沈阳自动化研究所,辽宁沈阳110016 [2]中国科学院机器人与智能制造创新研究院,辽宁沈阳110016 [3]中国科学院大学,北京100049 [4]广州大学机械与电气工程学院,广东广州510006 [5]沈阳化工大学环境与安全工程学院,辽宁沈阳110142

出　　处：《控制理论与应用》2020年第9期1904-1912,共9页Control Theory & Applications

基　　金：国家自然科学基金项目(61773366);辽宁省自然科学基金项目(2019–KF–03–07);辽宁省博士启动基金项目(20180540066);工信部工业互联网创新发展工程及智能制造综合标准化与新模式应用项目;广东省重点领域研发计划项目(2020B0101050001)资助。

摘　　要：预测控制算法的计算复杂度主要由变量个数和控制时域决定,而大型复杂系统中变量个数较多将导致计算量大的问题,尤其在有约束预测控制的优化求解中增加较重的计算负担.本文针对此问题利用邻接矩阵、可达矩阵和关联矩阵梳理系统传递函数模型中变量之间的关联,将有关联的控制变量划分为一个子系统,进而将一个大系统分解成若干独立子系统,即可将一个高维度的优化求解问题分解成多个维度较低的子优化问题,降低计算复杂度以达到减少计算量的目的.最后将其应用在多变量有约束的双层结构预测控制算法中,通过仿真进行验证.The computational complexity of the model predictive control algorithm is principally determined by the number of variables and the control time domain.While substantial variables in large-scale complex system will result in the problem of a great deal of computation,in particularly increasing computing burden in the optimization solution of constrained predictive control algorithm.In allusion to the problem,this paper employs adjacency matrix,reachability matrix and correlation matrix to sort out the associations among variables in the transfer function model of the system so that the related control variables are divided into the same one subsystem.Then decompose a large-scale system into divers independent subsystems.And a high dimensional optimization problem will be decomposed into several low dimensional sub optimization problems in order that decrease the computational complexity and the calculation.In the end of the paper applies the method to the multivariable constrained double layered structure predictive control algorithm and verified by simulation,which provides a new idea for the multivariable decomposition method.

关 键 词：预测控制 图论 计算复杂度 系统分解 

分 类 号：O231[理学—运筹学与控制论]