Design of Takagi-Sugeno Controllers Using Piecewise Constant Functions and a Normalized Fuzzification Transform
Takagi-Sugeno fuzzy controllers are today one of the most promising technique to describe input-output relations of nonlinear systems using fuzzy rules. This chapter presents an extension of this modelling technique mainly based on the use of global fuzzy parameters and convolution operators to specify different uncertainties of a system: imprecision of inputs, vagueness of antecedent linguistic labels and smoothness requirements of outputs. The presented approach provides an efficient method to specify and implement an extended zero order product-sum Takagi-Sugeno controller with fuzzy inputs, antecedent terms fuzzy partition with an additional uniform vagueness, and singletons outputs with an additional output filter. It introduces a similarity transformation that greatly simplifies the involved computation. The most relevant feature of this approach is a global transformation of imprecision of inputs, uniform vagueness of antecedent terms and smoothness requirements of outputs into a single convolution transform applied to the corresponding antecedent terms partition. The kernels of the fuzzification transforms used are even B-spline functions. Some practical considerations and examples are also given.
KeywordsFuzzy Number Fuzzy Rule Fuzzy Controller Linguistic Term Fuzzy Logic Controller
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