Fixed-time adaptive fuzzy control for time-varying systems based on nominal substitution

This paper addresses the problem of fixed-time control and pre-described tracking performance design for time-varying uncertain nonlinear systems. Unlike the pure robust control, the proposed so-called nominal substitution method avoids unnecessarily high gain and noise amplification. The control problem for n-dimensional time-varying uncertain nonlinear systems is discussed to show how to combine the nominal substitution method with adaptive fuzzy fixed-time control and a singularity-avoidance virtual controller design. To achieve pre-described tracking performance in a fixed-time convergence environment, a projection operator-based adaptive algorithm and a series of symbolic-like functions are introduced in the control design. It is shown that the proposed control method can guarantee that the tracking error asymptotically converges to a user-defined accuracy within a pre-described fixed time. Two simulation results, including comparison experiments and analysis of practical examples, verify the effectiveness of the proposed method.