Neuroadaptive Control Design for Pure-Feedback Nonlinear Systems: A One-Step Design Approach

In this article, we propose a one-step control design approach for pure-feedback nonlinear systems in the presence of unmatched and nonvanishing external disturbances. Different from the commonly utilized backstepping design, the proposed method, integrated with the dynamic surface control (DSC) technique, only involves one-step design with one single Lyapunov function in the whole control synthesis, which derives the actual control and the intermediate controls simultaneously in a collective way, avoiding the repetitive design procedures and multiple Lyapunov functions, yet circumventing the issue of "explosion of complexity." Furthermore, with this method, the increase in system order does not increase the design and analysis complexity. Numerical simulation examples confirm and validate the effectiveness of the proposed method.