Design of Wavelet Adaptive Backstepping Controller for Uncertain Systems

This paper proposes an adaptive wavelet backstepping controller for nonaffine nonlinear systems. The backstepping design scheme for the high order system has a complexity explosion problem that will lead the basis of virtual controller differentiation constantly. For solving this problem, this paper uses the first order filter at each sub-system of the backstepping controller. Moreover, the adaptive wavelet backstepping controller can approximate the linearization system through the mean value theorem, which is also used to avoid a higher order problem derived from Taylor linearization expansion. Finally, Lyapunov equation can guarantee the stability of the closed loop system. The simulation results are confirmed to illustrate the effectiveness and applicability of the proposed method.