Control of switched systems with delayed states: A direct AFSMC approach

Abstract

This research focuses on controlling a class of MIMO state-delayed nonlinear systems with switching conditions that depend on the delayed states. The key concept is to consider the dynamic changes brought by switching between sub-systems as an uncertainty bounded by a certain polynomial of the delayed states norm. The challenge of managing a delayed switched system is changed to the simpler problem of controlling a delayed non-switched system via an extended AFSMC approach with just one sliding surface. New adaptation laws are proposed within the general framework of the direct AFSMC scheme to estimate unknown coefficients of the uncertainty bound polynomial and parameters of a central fuzzy controller, which mimics the behavior of a feedback linearized controller in the conventional SMC approach. Using the method of multiple lyapunov-krasovskii functions (MLKF), closed-loop stability is proven. Several examples are elaborated to show the effectiveness of the method compared to the previously proposed no-delay AFSMC method and also to the conventional feedback linearization approach. In particular, the proposed control scheme is applied to a benchmark high-speed super cavitation underwater vehicle. The efficacy of the proposed method is depicted, while minimal information about the plant dynamics is needed in the control design stage.