Adaptive Fuzzy Prescribed Finite-Time Tracking Control for Nonlinear System With Unknown Control Directions

This article investigates the prescribed finite-time control for the nonlinear system with uncertain nonlinearity and unknown control directions. Different from the existing finite/fixed-time control methods on the basis of the fractional-order state feedback, the proposed finite-time control in this article only employs regular state feedback. The key is that a novel prescribed finite-time performance function is introduced such that the controller design is under the standard Lyapunov stability theoretical framework. A lemma is developed as a tool for coping with the coexistence of multiple Nussbaum gains for the stochastic system with unknown control directions. Fuzzy logic systems are used to approximate the uncertain nonlinear functions. Applying the backstepping structure, an adaptive fuzzy control scheme is developed. The salient characteristic of the proposed control is that the finite convergence time and the accuracy of the tracking error are independent of the initial states and design parameters, and that can be assigned in a prior. Two examples are given to demonstrate the feasibility and effectiveness of the proposed control scheme.