Modeling Problems In Nonlinear Predictive Control

Predictive control is a control method based on but not confined by the model. Building prediction model is essential and critical to predictive control. Due to the lack of unified model description, predictive control of various nonlinear systems is based on the model description of different nonlinear systems. Therefore, it is necessary to study modeling in nonlinear system predictive control. Several kinds of modeling method of A Class of nonlinear system are presented in this paper, and based on these non-linear modeling methods, several kinds of predictive control algorithms of nonlinear system are introduced.A simple polynomial approach for A Class of nonlinear system modeling is presented. By this, the input-output data are firstly changed into [0, 1] by using topological homeomorphism conversion; then an initial polynomial model is selected. The parameters of polynomial model are estimated by using recursion least squares method. A final polynomial model is obtained by repeatedly estimating parameter and eliminating redundant terms. A predictive control algorithm based on polynomial approach modeling is proposed. For nonlinear system, a series of nonlinear output prediction models with different prediction steps are obtained by polynomial approach of nonlinear modeling. Solving predictive control law is turned into solving group of equation by optimizing objective function. The predictive control law is modified by pre-step predictive control error.Fuzzy modeling method is studied and two kinds of improved fuzzy modeling methods are presented. In improved nearest neighborhood cluster fuzzy modeling, accuracy is achieved by dynamically updating radius of cluster and the variance parameter. In improved T-S fuzzy modeling method, the number of clusters and clustering center are obtained first by improved nearest neighborhood cluster; then, antecedent parameters are obtained by Gustafson-Kessel fuzzy clustering and consequent parameters are identified by least square with forget factor; finally, a model is obtained by acquiring the important rules and removing the less important rules. A fuzzy predictive control method based on improved T-S fuzzy modeling method thus is acquired. A series of predictive model is obtained by improved T-S fuzzy modeling method. The model includes input and output data before current time and future input value. This method does not need to solve Diophantine equation and nonlinear programming.Research on multi-layer recursive is used in modeling and forecasting of A Class of nonlinear system. A multi-layer recursive adaptive predictive control method is presented for nonlinear discrete system. In this method, nonlinear system is substituted by a time-varying linear system firstly, and then multi-layer recursive is used to identify and to forecast the varied parameters in order to get the predictive output of system model. At last, adaptive predictive control is designed for the original nonlinear system. This method does not need to solve Diophantine equation and does not need to depend on model of nonlinear system.For A Class of nonlinear system, a model free predictive control is presented. This method does not need modeling in the predictive control. The eigenvector of general model is identified and predicted by multi-layer recursive method. With function combinations, the model free predictive control law has the same advantages as model free control does.