Fuzzy Functional Observer-Based Finite-Time Adaptive Sliding-Mode Control for Nonlinear Systems With Matched Uncertainties

Abstract

This article is concerned with the fuzzy functional observer-based finite-time adaptive sliding-mode control for nonlinear systems with the partly unmeasurable states and some matched uncertainties. First, considering that the upper bound of the uncertain function exists but unknown, a fuzzy functional observer (FFO) with an adaptive compensator is constructed. Second, an FFO-based fuzzy integral sliding mode controller (ISMCr) is designed such that the closed-loop fuzzy systems are finite-time bounded with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance over the reaching phase, the sliding phase, and the whole finite-time interval, respectively. To reduce the conservatism and increase the solution space of linear matrix inequality conditions, the fuzzy Lyapunov functional approach and equivalent fuzzy relaxed matrices technique are developed by introducing some relaxed matrices in the derivative of the fuzzy normalized membership function. Compared with the common Luenberger-type observer-based approach, the gain matrices of ISMCr depend on the FFO designed, which also enhances the flexibility of controller design. Finally, a simulation example with some comparison is given to show the effectiveness of the proposed method.