Dynamic backstepping control for pure-feedback nonlinear systems
Solves a known bottleneck in backstepping control for a specific class of nonlinear systems (pure-feedback), offering an incremental improvement over traditional methods.
Proposed a dynamic backstepping method for pure-feedback nonlinear systems that avoids solving implicit algebraic equations by augmenting virtual controls as states, achieving uniformly asymptotically stability with demonstrated effectiveness in stabilization and tracking examples.
A dynamic backstepping method is proposed to design controllers for nonlinear systems in the pure-feedback form, for which the traditional backstepping method suffers from solving the implicit nonlinear algebraic equation. The idea of this method is to augment the (virtual) controls as states during each recursive step. As new dynamics are included in the design, the resulting controller is in the dynamic feedback form. Procedure of deriving the controller is detailed, and one more Lyapunov design is executed in each step compared with the traditional backstepping method. Under appropriate assumptions, the proposed control scheme achieves the uniformly asymptotically stability. The effectiveness of this method is illustrated by the stabilization and tracking numerical examples.