Adaptive Fuzzy Control for Stochastic Nonlinear Systems With Nonmonotonic Prescribed Performance and Unknown Control Directions

This article presents an adaptive fuzzy control scheme capable of guaranteeing prescribed performance for stochastic nonlinear systems with unknown control directions. Unlike the majority of existing prescribed performance control schemes, the proposed scheme ensures the independence from initial errors and guarantees controllable overshoot. Moreover, the proposed prescribed function exhibits nonmonotonicity, which can be beneficial in control applications with input constraints. To address the challenge posed by unknown control directions, a novel class of multiple Nussbaum functions is introduced. Compared to the existing single Nussbaum function, the multiple Nussbaum functions can mitigate instability arising from the cancelation of multiple unknown signs. Additionally, to tackle unknown nonlinearities, a single-parameter fuzzy approximator is introduced, aiming to concurrently reduce computational complexity. Furthermore, a novel class of switching threshold event-triggered mechanisms is designed to address issues encountered in existing designs where parameter inequalities impose conservative constraints. The control scheme ensures that the tracking error converges to prescribed asymmetric boundaries with arbitrarily small residuals in a prescribed time, while also guaranteeing that all closed-loop signals are bounded in probability. The effectiveness and superiority of the control scheme are verified by simulation results.