Practically Fast Finite-Time Stability in the Mean Square of Stochastic Nonlinear Systems: Application to One-Link Manipulator

A fast finite-time adaptive fuzzy tracking control algorithm is proposed for stochastic nonlinear systems (SNSs) under an event-triggered mechanism. Unlike the traditional finite-time control of SNSs, for this article, the drift and diffusion terms can be completely unknown. First, a fuzzy-logic system has been implemented to approximate the uncertain functions of SNSs. Second, a novel theorem of a fast finite-time adaptive control mechanism of deterministic systems is presented by revamping the fast finite-time stability in the mean square. Next, the complex explosion issue caused by the backstepping technique is effectively avoided based on command filtering feedback control. Compared with the standard backstepping technique, which has avoided the analytical computations of the derivatives of virtual control functions and has dramatically reduced the computational burden. Finally, an example of the one-link manipulator with motor dynamic systems is provided to verify the theoretical analysis.