Adaptive fuzzy prescribed time tracking control for nonlinear systems with input saturation.

This article investigates the adaptive fuzzy prescribed time tracking control problem for a class of strict-feedback systems simultaneously considering the user-defined asymmetric tracking performance, input saturation, and external disturbances. From the perspective of ensuring the reliability for control implementation, a saturation-based fixed-time funnel boundary is constructed by embedding the modification signals related to input saturation errors into a funnel function, which is capable of automatically enlarging or recovering itself when input saturation occurs or disappears, thereby reducing the risk of system singularity. Subsequently, by constructing a fixed-time tracking performance function, any known bounded tracking error is recast into a new variable with a zero initial value. With such a treatment, funnel boundaries are no longer redeveloped for different initial tracking errors, and meanwhile the behavior of the tracking error is pre-specified as needed over a finite time interval. Also, auxiliary systems are devised to generate the aforesaid modification signals, while compensating for the adverse impact resulting from input saturation. Remarkably, by feat of the backstepping design based on the fuzzy approximation, it is proven that the tracking error converges to a user-defined region within a prescribed time (known as the practically prescribed time tracking), which is achieved without the fractional power feedback of system states. Finally, two simulation examples are presented to confirm the feasibility and effectiveness of the developed approach.