Modeling And Control Of PWA Systems Based On Constrained Clustering

PWA model is an important class of hybrid systems,which separates the regression region into a finite number of non-overlapping partitions.Linear models are estimated from datapoints of each subregion to describe dynamic characteristics.PWA systems can approximate general nonlinear dynamics with arbitrary precision and provide an equivalent representation for other hybrid models.Therefore,they are widely used in production and daily life.The controller can be designed according to the identified PWA model for hybrid systemThe clustering-based identification method is commonly used,containing the classification of datapoints?the estimation of sub-models and the partition of regression region.In traditional clustering-based techniques,data classification and region partition are performed independently so that inseparable problem usually occurs in region estimation.In order to solve these problems,the main research work is as follows:1)The identification algorithm of one-dimensional PWA model based on constrained K-means clustering is proposed.The data classification and region partition are performed simultaneously by imposing the complete and non-overlapping partition constraints into the clustering optimization problem.Inseparable problem can be avoided,and the method can greatly the accuracy of PWA model.Simulation verifies the effectiveness of the proposed algorithm.2)The identification algorithm of multi-dimensional PWA model based on constrained grid hierarchical clustering is proposed.Inspired by the intelligent optimization algorithm,the random dividing strategy is introduced into the agglomerative clustering process to avoid hierarchical clustering from falling into local optimal solution.The constrained agglomeration and constrained division are realized by adjacency matrix techniques of undirected graphs,automatically achieving the complete and non-overlapping partition of regression region.Results of simulation illustrate that the proposed algorithm is a feasible way to improve the accuracy of PWA model3)The Convex Hull is employed for the identified PWA model to construct the smallest convex hull containing each subregion,and the hybrid MPC controller is based on MLD framework.Results of simulation verify the effectiveness of MPC controller.