Adaptive Backstepping Control for Nonlinear Systems Using Support Vector Regression

A nonlinear adaptive backstepping control approach is designed for a class of n-th order nonlinear systems. Support Vector Regression (SVR) is employed to adaptively approximate the unknown nonlinear functions composed of unknown uncertainties and disturbances. Unlike neural networks, no number of hidden units has to be determined for the controller and that no centers have to be specified for the Gaussian kernels when applying Mercer's condition. The curse of dimensionality is avoided in comparison with defining a regular grid for the centers in classical radial basis function networks. The closed-loop system is guaranteed to be bounded and tracking errors are also proved to converge exponentially to a small residual set around the origin by Lyapunov theory. Simulation results demonstrate the effectiveness of the approach proposed.