Fuzzy approximation-based adaptive finite-time control for nonstrict feedback nonlinear systems with state constraints

Abstract This paper solves the adaptive fuzzy finite-time control (AFFTC) problem for nonstrict feedback nonlinear systems with state constraints. Different from the recently works that mainly focus on the C 0 finite-time design scheme, in our context, an innovative C 1 AFFTC method is created by combining the fuzzy approximation with backstepping technique. The singularity problem existing the traditional finite-time scheme is skillfully tackled by creating the smooth switch function. The barrier Lyapunov function is exploited to make all states maintain the predefined regions. By means of Lyapunov stability analysis, the devised AFFTC can make all error signals converge into a small neighborhood of the zero in a finite time. Finally, simulation results illustrate the validity of the designed method.

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