Command Filter Based Adaptive Fuzzy Finite-Time Control for a Class of Uncertain Nonlinear Systems With Hysteresis

Abstract

This article addresses an adaptive fuzzy finite-time control for a class of uncertain strict-feedback nonlinear systems with backlashlike hysteresis and stochastic disturbances. At first, a novel criterion of semiglobally finite-time stability in probability (SGFSP) is established based on Lyapunov function method. Under the proposed stability criterion, an adaptive fuzzy finite-time control scheme is designed. In the design process of the controller, command filter technique is introduced to overcome the problems of “explosion of complexity” and “singularity” inhered in the traditional adaptive finite-time control based on the backstepping method. Meanwhile, via constructing the corresponding error compensating systems, the effect of errors generated by the command filters is reduced, such that the original systems have more better tracking performance. To cope with the influence of backlashlike hysteresis input, an auxiliary system is constructed, in which the output signal is applied to compensate the effect of the hysteresis. It is shown that the tracking error can converge to a small neighborhood of original in finite time, and the closed-loop system is SGFSP under the constructed controller. Finally, the effectiveness of the proposed control strategy is further verified by two simulation examples.