Data-based Real-time Solutions And Tracking Control For Nonlinear Systems

Affine nonlinear system is a commonly used important form of nonlinear system and also is one of research hotspots in control field.Many systems in practical engineering can be expressed as the form of affine nonlinear systems,so the research of this system has important theoretical significance and engineering significance.In this thesis,a kind of on-line unbiased least squares support vector machine algorithm is adopted to solve the problem of real-time and tracking control for a class of partially unknown affine nonlinear systems.In this thesis,the online unbiased least squares support vector machine algorithm is a combination method,which is based on the least squares support vector machine combined with the method of eliminating bias,rolling time window method and weight optimization function.The least squares support vector machine is used to construct the frame of the algorithm.The method of eliminating bias and weight optimization is used to improve the precision and efficiency of the algorithm.The algorithm can be used to process the on-line data in real time by rolling time window method.The main work of this thesis has three aspects:1.This thesis combined with unbiased idea,a constant is introduced into the regression form of least squares support vector machine,and the bias term is incorporated into the weight vector in the form of regression,which is eliminated in the form of the matrix.The coefficient matrix of the linear equation group which makes the final requirement is reduced to the compact matrix from the sparse matrix,which avoids many redundant computations,and improves the efficiency and accuracy of the algorithm.2.This thesis using the rolling time window method to realize the real-time on-line function of the system solving and tracking control in this kind of system.At the same time,an error threshold is set up in the rolling time window to determine whether each rolling solution needs to be re-established to solve the model,which can reduce the number of modeling,save computation time and speed up the algorithm.3.Weight function is introduced into the optimization objective of the model.Because the sample point closed to current moment in the rolling time window have greater impact on the accuracy of the approximate solution of next moment,so the training sample points in the rolling time window are given different weights,which makes the accuracy of the algorithm is further improved.