多变量预测控制结构分解的图论方法

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.

Graph theory method for multivariate predictive control structure decomposition

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.