Adaptive Dynamic Surface Control for a Class of Pure-Feedback Nonlinear Systems

A novel adaptive dynamic surface control approach is proposed for a class of completely nonaffine pure-feedback nonlinear systems. Based on the mean value theorem, the unknown non-affine input functions are decomposed into new ones with explicit controllable input parameters. The Nussbaum gain function is employed to resolve the unknown gain symbol problem in virtual control, and avoid the possible singularity of the controller in feedback linearization process. The explosion of terms problem in traditional backstepping design is eliminated by utilizing dynamic surface control. Based on Lyapunov stability theorem and decoupled backstepping method, the semi-global stability of the close-loop system is proved. Simulation results show the effectiveness of the proposed approach.