Adaptive Control Of Nonlinear System Based On Support Vector Machine

Support Vector Machine (SVM), which is based on the ideal of VC dimension and StructuralRisk Minimization (SRM), is a general pattern recognition algorithm with high generalizationability. Therefore, it has many unique advantages when dealing with the small samples andnonlinear pattern recognition problems. With the in-depth study of SVM, it has been extendedto the function regression and other learning problems. With the in-depth study of SVM, it hasbeen applied to some other learning problems such as fuction regression. It has beenintroduced into the field of system identification and controller design, because of itspowerful nonlinear regression ability. At present, it already had some achievements in thefield of system identification and predicte control of nonlinear system based on SVM, butthere are few results of adaptive control of nonlinear system based on SVM.In this thesis, we will study the adaptive control of a class of SISO affine nonlinear systemcombined with support vector machine. The main contents of the thesis are outlined asfollows:i. First, reviewed the core ideal of SVM—ideal of the optimal hyperplane, then explainedthe basic principles of support vector regression (SVR) and its applications in control.ii. Present an online algorithm for support vector regression based on Subgradientprojection in reproducing kernel Hilbert spaces. Firstly, we choose the distance merticbetween the model and the neighborhood space of a sample data to characiterize theempirical risk of support vector machine learning, and formulate a new expression ofsupport vector regression sequentially. Secondly, we obtain the online algorithm forsupport vector regression based Subgradient projection by introducing in the concept ofprojection and subgadient. The simulation of Mackey Glass system shows that itconverges fast and the computational complexity is simple. It can be well used to theadaptive controller design of nonlinear system.iii. Based on the online algorithm for support vector based on Subgradient projection, wedeveloped an adaptve state feedback controller and an adaptive output feedbackcontroller for a class of SISO affine nonlinear systems using support vector regression.iv. We applied the results abtained in the thesis to the inverted pendulum control system, developed an adptive state feedback controller. Simulation results had confirmed theusefulness of the controller.