This article extends the finite-time adaptive tracking control to stochastic nonlinear systems with multiple uncertainties, including output constraints, unknown parameters, unmodeled dynamics and external disturbances. Most relevant results in the literature have two main restrictions: 1) uncertainties and unknown items in the systems; 2) the matter of “explosion of complexity”. By integrating an improved technique of adding fuzzy logic systems to estimate unknown parameters with a bounded command filter method, a systematic tracking control scheme is developed that eliminates both of the above restrictions. To alleviate the serious uncertainties caused by the constraints, a quartic asymmetric time-varying barrier Lyapunov function is utilized when the control coefficient is known. Subsequently, an event-triggered controller is constructed that enables boundedness and finite-time convergence of all closed-loop signals. Eventually, to validate the effectiveness of the proposed adaptation strategy, this new method is applied to ship maneuvering systems that encounters multiple uncertainties arising from disturbances such as wind, waves, and ocean currents.

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.