Generalized Predictive Control Algorithm Based On Least Squares Support Vector Machines

A large number of industrial produce processes have a nonlinear, uncertainand time-varying characteristics, however the tradition control theoriesestablished by precise mathematic model of the plants, so that it is difficult toestablish a precise analytical model, lead to effects of control is not well. Inorder to overcome those problems, Model Predictive Control (MPC) as a newlycontrol arithmetic arouse widely recognition of domestic and foreign controltheory. MPC is based on control strategies of forecasting model, rollingoptimization and feedback correction, so it has a good controllability,robustness.Aim at nonlinear decontrolled plants at large exist in industrial processes,this thesis bring forward arithmetic of nonlinear generalized predictive controlalgorithm based on least squares support vector machines.Generalized predictive control (GPC), aroused by Clarke etc, is a adaptivepredictive control algorithm which developed by traditional minimum variancecontrol and adaptive control, GPC is Based on traditional controlledauto-regressive integrated moving average (CARIMA) model, hold true timedelay and non-minimum phase object, and improve control performance androbustness of model unmatched, and use long periods optimize performance cost, have characteristics of strong robustness and low request to model.Now , GPC based on linear predictive model is successfully used in industrial control, but GPC based on nonlinear predictive model, require controller resolve a nonlinear programming problem at every sampling period, which size is relate to parameters of predictive model。Due to the difficulties in modeling to nonlinear system and on-line rolling optimization, this problem is still only a open issue.Now commonly used non-linear predictive models, include neural networks fuzzy models and so on, which learning algorithms are based on empirical risk minimization principle. But there are still some difficult problems to solve, such as difficult to determine the hidden layer nodes of neural networks, the phenomenon of over fitting, local minimum problems in the training process and so on. Recently Vapnik and others propose support vector machine (SVM) become hotspot of nonlinear modeling, SVM is based on VC dimension theory of statistical learning theory and structural risk minimization principle, SVM Characteristics of automatically design model with a complexity and high generalization ability, training algorithm don't have local minimum problem, and have good effect to approximation to nonlinear plant model. But with the increasing of training samples, SVM will be faced with the curse of dimensionality, leading to no training. With an increase of the error sum of squares of items in the standard SVM objective function, Suykens JAK propose least squares support vector machine (LS-SVM) method, which change inequality constraints into equality constraints, the optimization problem into a linear equation, bias in a square into two parties of experience in risk, LS-SVM overcome the classic quadratic programming method for solving support vector machines curse of dimensionality problem, and has a good robustness, suitable for large-scale computing. So use LS-SVM as nonlinear predictive model have more advantages.This thesis will use LS-SVM model and simulate to nonlinear system, and comparison with BP neural network, the simulate results show that LS-SVM has the same model precision and high generalization ability to BP neural network. Then I use GPC carry through predictive control to LS-SVM predictive model and BP neural network, simulate results that the algorithm propose by this thesis have good performance to nonlinear system.Then I use GPC based on LS-SVM to predictive and simulate to a issue of typical strongly nonlinear systems, continuous stirred tank reactor CSTR. the simulation results present that the generalized predictive control algorithm proposed in this paper which based on the least squares support vector machine has a good validity.