Adaptive dynamic surface control for a class of time-varying uncertain nonlinear systems and application

On the basis of the traditional backstepping, the dynamic surface control technique can simplify the backstepping design and overcome the complexity due to the “explosion of terms” by introducing n-1 low pass filters. In this paper, an adaptive dynamic surface control based on the function approximation with Fourier series is proposed for a class of time-varying uncertain nonlinear systems. The uncertainties are assumed to be piecewise continuous functions of time and satisfy the Dirichlet conditions. By representing these uncertainties in finite-term Fourier series, they can be estimated by updating the Fourier coefficients. Our development is able to not only eliminate the problem of “explosion of complexity”, but also estimate the time-varying uncertainties with unknown bounds online. The proposed control law can guarantee the tracking error with arbitrarily small. At last, the method is used to design the controller of Buck DC switched power converters.