Echo state network-based adaptive control for nonstrict-feedback nonlinear systems with input dead-zone and external disturbance

This paper addressed the adaptive control problem for non-strict-feedback nonlinear systems with dead-zone and external disturbances. The design methodology integrated the backstepping technique with the approximation of unknown functions using an echo state network (ESN), enabling real-time adjustments. A comprehensive Lyapunov stability study was conducted to confirm the semi-globally uniformly ultimately boundedness (SGUUB) of all signals in the closed-loop system, ensuring that the tracking error converged to a small neighborhood of the origin. The effectiveness of the proposed method was further demonstrated through two examples, and error assessment criteria were utilized for comparisons with existing controllers.