Approximate Solutions And Optimal Tracking Control For Nonlinear Systems Based On LS-SVM

Nonlinear systems appear in various fields of natural science and engineering technology,which have been concerned all the time.Due to the high nonlinearity,unknown dynamic characteristics and uncertainty of the model,obtaining the solution of nonlinear problems is very complicated.With the continuous development of intelligent algorithms such as machine learning,there are some new approaches to solve nonlinear problems.This thesis mainly studies how to solve the initial value problem of nonlinear ordinary differential equation and achieve the optimal tracking control for affine nonlinear system by least squares support vector machine(LS-SVM)approach in machine learning.The main research contents are as follows:1.An improved approach based on least squares support vector machine is proposed for solving nonlinear ordinary differential equations and second-order nonlinear ordinary differential equation with initial conditions.Firstly,the parametric form of approximate solution is given.Secondly,LS-SVM model is improved by using the differentiable radial basis function(RBF)and transform the model which includes the derivative form of RBF into an optimization problem to solve.Finally,we can obtain the approximate solution with optimal parameter value.The proposed approach can obtain the optimal representation of the solution in the primal-dual setting and provides a continuous-differential form approximate solution with high accuracy.In addition,numerical experiments are presented and compared with exact solution to confirm the validity and accuracy of the proposed approach.2.In this paper,a data-driven approach based on least squares support vector machine is proposed to design optimal tracking controller for affine nonlinear systems.According to the information of the system and discrete data of the desired trajectory,the LS-SVM model is employed to obtain the approximate solution of optimal tracking trajectory and achieve optimal tracking control,which allows the system has the desired dynamic performance.The proposed approach is an intelligent control method with optimization and learning ability and the system can track the desired trajectory in a small error bound.In addition,numerical simulation examples are provided to verify the accuracy and effectiveness of the approach.