Analysis and synthesis of fuzzy linguistic control systems
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abstract
In this paper we present a new conceptual framework for design and analysis of fuzzy linguistic control systems. Specifically, by parametrizing the characteristic functions of fuzzy subsets describing the linguistic terms used in the definition of the control law, we develop an analytic formulation of the control scheme. Further, we use this analytic form to derive sufficient conditions for the stability of the system. We will also establish the connection between fuzzy control and a class of nonlinear control schemes, namely those with piecewise linear characteristics, and present a new interpretation of fuzzy control that helps explain how certain types of nonlinearities, such as asymmetric response characteristics, can in effect be canceled by appropriate formulation of control rules. Finally, we discuss the broader implications of this analytic formulation and raise some issues for future research in this area.
