Robust Adaptive H∞ Controller Based on Hybrid Genetic Wavelet Kernel Principal Component for Nonlinear Uncertain Systems

In this paper, two adaptive H∞ control schemes based on a genetic wavelet kernel support vector machine (SVM) and a hybrid genetic wavelet kernel SVM is presented for nonlinear uncertain systems. In these methods, wavelet kernel SVM is employed to establish the adaptive controller and an on-line learning rule for the weighting vector and bias is obtained. The H∞ control technique is combined with adaptive control algorithm and wavelet support vector machine to achieve the desired attenuation on the tracking error caused by wavelet-SVM approximation error and external disturbances. The most important characteristic of this strategy is its intrinsic robustness and its ability to treat the nonlinear behavior of the system. The results of simulation show that this SVM online algorithm controller is very effective and the SVM controller can achieve a satisfactory performance.