Adaptive recursive gain asymptotic tracking of uncertain nonlinear systems with time-varying parameters and disturbances

This paper focuses on achieving adaptive asymptotic tracking for a class of uncertain nonlinear systems. These systems are distinct from those examined in previous studies due to the presence of unknown time-varying parameters and disturbances. By combining adaptive techniques and recursive gain control, an adaptive tracking controller is successfully devised to accomplish asymptotic tracking. An important distinguishing feature of the proposed controller is its integration of a smooth function with a time-varying function that is both integrable and positive. This integration endows the controller with the capability to effectively compensate for unknown time-varying parameters and disturbances. Notably, a Lyapunov function is used to establish the closed-loop system stability. Simulation results validate the effectiveness of the presented control, surpassing command filter adaptive asymptotic backstepping control and dynamic surface adaptive asymptotic control, addressing the challenge of the ‘explosion of complexity,’ and achieving asymptotic tracking despite the existence of time-varying parameters and disturbances.