Adaptive learning control for a class of uncertain nonlinear systems

An adaptive learning control algorithm is developed for a class of high-order nonlinear systems with both parametric and non-parametric uncertainties. The unknown time-varying parameters are estimated by a periodic repetitive learning strategy. To tackle the non-parametric uncertainties, the unknown periodic reference input signal is expanded with the sum of finite Fourier series and bounded truncation error, which is adaptively learned by estimating its Fourier coefficients. The hyperbolic function is introduced to eliminate the influences of truncation errors. By constructing a Lyapunov-like function, we prove the boundedness of all signals and the convergence of the tracking error. The results are extended to nonlinear systems with unknown control coefficient. Two simulation examples are supplied to illustrate the effectiveness of the proposed control scheme.