A Chattering-Free, Adaptive, Robust Tracking Control Scheme for Nonlinear Systems With Uncertain Dynamics

This paper introduces a chattering-free, adaptive, and robust tracking control scheme for a class of second-order nonlinear systems with uncertain dynamics. First, a proportional-integral-derivative control-fast terminal sliding function is proposed to enable the advantages of both the PID and non-singular fast terminal sliding mode approaches in the field of non-singularity, fast convergence time, defined time convergence, and stability with small steady-state errors. Second, to obtain the desired control target without chattering behavior, the proposed controller with a continuous approach has been applied. In detail, the proposed controller uses an integral of a switching term and an adaptive updating law to compensate the lumped system uncertainty (e.g., disturbances, unmodeled dynamics, nonlinearities, or unmeasurable noise). Our proposed controller does not require knowledge about bound values of those anonymous components. The robust behavior and the defined time convergence have been demonstrated rigorously by the Lyapunov principle. Finally, the position tracking computer simulations have been performed to demonstrate the effectiveness and practicality of the suggested controller.