An Associatively Recursive Dynamic Backstepping Control Design for Pure-Feedback Nonlinear Systems

An Associatively Recursive Dynamic Backstepping Control (ARDBC) method is proposed for nonlinear systems in the pure-feedback form. By transforming the plant to the pseudo-strict-feedback form that has affine appearance of state variables to be used as the virtual controls, it circumvents the implicit algebraic control equation arising from applying the traditional backstepping method and avoids the introduction of dynamics for virtual controls as Zhang et al. (2019), in that only the actual controls are treated as augmented states to derive the dynamic feedback control law. Therefore, the design procedure is facilitated and the controller form is simplified. Under appropriate assumptions, the proposed control scheme achieves the uniformly asymptotical stability. The effectiveness of this method is illustrated by the stabilization and tracking numerical examples. In addition, the comparison to its previous counterpart is drawn, which shows its rigorous requirement on the preconditions in application.