A Practical Predefined-Time Stability Criterion and Its Application to Uncertain Nonlinear Systems

In this paper, the singularity-free predefined-time fuzzy adaptive tracking control problem is studied for non-strict feedback (NSF) nonlinear systems considering mismatched external disturbances. An innovative practical predefined-time stability (PPTS) criterion is proposed to provide the theoretical basis for subsequent control design. Compared to the existing predefined-time stability (PTS) criterion, this criterion has a broader application range and can solve the control design issues of nonlinear systems with system uncertainties. Fuzzy logic systems (FLSs) are employed to identify unknown nonlinear functions. Based on the backstepping control technology, a singularity-free predefined-time control (PTC) design method is proposed, in which the hyperbolic tangent function is utilized to avoid the singular problem, and the nature of fuzzy basis function is adopted to resolve the algebraic loop problem. The PPTS of the closed-loop NSF nonlinear system is proven with the Lyapunov theory and the proposed PPTS criterion. Ultimately, the efficiency of the presented PTC design method is verified by several sets of simulations on a single link manipulator system.