Fixed-Time Adaptive Control for Nonstrict-Feedback Nonlinear Systems with Input Delay and Unknown Backlash-Like Hysteresis

This article explores the tracking control challenge within nonstrict-feedback nonlinear systems featuring input delay and unknown backlash-like hysteresis. A fixed-time adaptive control scheme is developed to address this problem. Radial basis function neural networks play a key role in identifying the unknown nonlinear functions during the design process. Pade approximation and an intermediate variable are strategically employed to mitigate the impact of input delay, while the compensation for the effect of unknown hysteresis input is achieved through approximating another intermediate variable. By combining the adaptive backstepping control technique with fixed-time stability theory, the article presents an adaptive fixed-time control method. The control scheme proposed ensures the boundedness of all signals in the closed-loop system, as analyzed through the Lyapunov stability theory. This guarantees accurate tracking of desired signals within a fixed time. The efficacy of the proposed approach is additionally validated through simulation studies. The effectiveness of the proposed controller is validated with a real-world example involving an electromechanical system.