A Study On Adaptive Control Methods Of Nonlinear Systems Based On Least Squares Support Vector Machine

Adaptive control for a class of nonlinear uncertain systems is a challenging problem all the time. Least squares support vector machines (LS-SVM) regression method based on Statistical Learning Theory (SLT) is a new powerful tool of identification and control for nonlinear systems. It overcomes the inherent problems of neural network and achieves higher generalization performence than classical neural network. It has been demonstrated that LS-SVM can uniformly approach an arbitrary nonlinear function to any desired degree of accuracy under certain conditions. So far, it has been broadly applied in many fields such as the modeling and control research for nonlinear systems. But, there are still many problems that need to be solved for practical implementations. Therefore, the history, progress and application of SLT and LS-SVM are reviewed first. Subsequently, some algorithms about the application of LS-SVM in nonlinear system modeling and adaptive control are presented in this paper.The main contributions of this thesis are listed as follows:1. A novel LS-SVM modeling method is presented based on chaotic ant swarm (CAS) algorithm with the hyper-parameter selection using LS-SVM to model the nonlinear systems. The CAS algorithm is used to the parameters optimization of LS-SVM. The hyper-parameter selection for LS-SVM is regared as a combinatorial optimization object function. The optimal parameters for LS-SVM are searched using the strong global search ability of CAS algorithm. This result will be applied to the subsequent research.2. A direct adaptive control method based on LS-SVM is developed for a class of single-input single-output nonlinear uncertain systems. The controller is designed based on the nonlinear feedback control theory, and then LS-SVM will be used to approximate the nonlinear dynamics. The adaptive laws for parameters of the controller are derived by Lyapunov theory, thus stability of the closed loop system is guaranteed. The corresponding indirect adaptive method is also presented. The stability of the closed loop system is established.3. A direct adaptive H∞control method based on LS-SVM is proposed for a class of nonlinear continuous systems with external disturbance. LS-SVM will be used to estimate the unknown nonlinear dynamics and construct the adaptive controller. H∞control is employed to compensate the effect on the tracking error caused by LS-SVM approximation errors and external disturbance. The stability and tracking performance of the closed loop system are ensured based on Lyapunov theory. The corresponding indirect adaptive method is also presented. The stability of the closed loop system is established.4. A direct adaptive output feedback control methods based on LS-SVM are proposed for a class of uncertain nonlinear systems with unavailable states and external disturbance. In this method, a state observer is designed to estimate the system states, and the LS-SVM is employed to construct the adaptive controller. H∞control is employed to attenuate the effect on the tracking error caused by LS-SVM approximation errors and external disturbance. The adaptive laws for parameters of the controller are derived on the basis of Lyapunov stability theory. Thus the stability of the proposed closed loop control system is guaranteed. The corresponding indirect adaptive method is also presented. The stability of the closed loop system is established.5. A method of robust adaptive tracking control based on LS-SVM dynamic inverse is developed for a class of nonlinear continuous systems with uncertain parameters. The method cascades the dynamic inverse model approximated by LS-SVM with the original system to get the composite pseudo-linear system. The on-line learning while controlling LS-SVM is used to adaptively regulate the error in the plant inversion which may be due to modeling uncertainties and disturbances. The updating rule of LS-SVM weight vector is derived from Lyapunov stability theroy. The stability of the desighed system is proved.