Smooth adaptive finite-time tracking for uncertain time-varying systems

This paper addresses the adaptive finite-time tracking control problem of strict-feedback nonlinear systems, where the control coefficient and the model parameters are time-varying and unknown. Based on the so-called congelation of variables method, a novel fractional-power adaptive update law is designed to achieve finite-time practical tracking in the presence of unknown time-varying coefficient/parameters. The virtual and actual control inputs of the proposed finite-time controller are designed in a smooth sign-function-like form complemented by a smooth sign-function-like filter, which allows for circumventing the singularity issues and the chattering phenomenon caused by non-smooth terms in classical finite-time controllers and filters. The tracking error proves to be bounded and converges to a desired compact set in finite time. Simulations of two practical examples are presented and show the effectiveness of the proposed algorithm.