A Nonlinear Formulation of a Class of Fuzzy Linguistic Control Algorithms

In this paper we present an analytic formulation of a general class of fuzzy linguistic control algorithms. This analytic formulation, which captures the essential nonlinearit(ies) of a given fuzzy control scheme, is based on using the characteristic functions of the rule set´s constituent fuzzy subsets as interpolating functions to shape a nonlinear function that maps the process error, and its rate of change or cumulative sum, into the appropriate control action. We will further discuss the implications of the proposed approach and its usage in establishing conditions for stability of fuzzy control systems, and in explaining how fuzzy control algorithms function as they do.