Adaptive dynamic surface control for unknown pure feedback non-affine systems with multiple constraints

In this study, an adaptive dynamic surface control scheme is developed for a class of nonlinear systems. The considered systems can be viewed as a class of unknown pure feedback non-affine systems with multiple constraints. One remarked advantage is that not only less adjustable parameters are used in the design but also the design structure is universal for different systems. The characteristics of the considered systems will lead to a difficult task for design a low-complexity and stable controller. To this end, the mean value theorem is employed to transform the pure feedback systems into a linear structure, but non-affine terms still exist. Then, a novel recursive design procedure is constructed to remove the difficulties of unknown model, pure feedback non-affine characteristic and multiple constraints by integrating two auxiliary elementary functions with a novel bounded estimation approach. Furthermore, based on Lyapunov stability theorem and decoupled back-stepping method, it is proved that all the signals in the close-loop system are global uniformly bounded and the tracking error satisfies prescribed transient and steady state performance indexes constraints. Finally, simulation studies clarify and verify the approach.