On the accessibility/controllability of fuzzy control systems

Abstract

Accessibility/controllability are very important concepts in the design of fuzzy logic control systems (FLCS) from both theoretical and practical perspectives. This paper proposes a systematic methodology that utilizes differential geometry/Lie Algebra, that has not been investigated in the literature, for analyzing the accessibility/controllability of TS FLCS. First, we linearize TS FLCS and show that this process, although it is straightforward, has limitations when analyzing some FLCS structures. Thus, we propose a novel algorithm by consolidating the linearization and Lie Algebra techniques that provides a systematic approach to assess accessibility/controllability. The advantage of the proposed algorithm is that in the case of nonaccessibility, those associated trajectories are found. The proposed approach is generic and does not require assumptions on FLCS’s rules or structures as is common with the few existing fuzzy systems controllability analysis methods in the literature. Moreover, we show that unlike exiting methods, our approach is not limited to small rule bases, but is also applicable for systems with large number of rules. To validate the effectiveness of the proposed method, we present several illustrative benchmark examples that will be of practical use to control engineers and can, as well, enable wider scale use of FLCS in various engineering applications.