Identification of Takagi-Sugeno Fuzzy Models via Clustering and Hough Transform

In this chapter we consider the identification of a Takagi-Sugeno fuzzy model (TS fuzzy model) [2]. This type of fuzzy model is especially useful in the area of fuzzy model-based control [10]. The TS fuzzy model is a nonlinear system model represented by fuzzy rules of the type (1.1)$$ {R^i}:If{x_1}isA_1^iand...and{x_m}isA_m^ithen{y^i} = a_0^i + a_1^i{x_1} + ... + a_m^i{x_m}$$ where Ri (i = 1, 2, …,n denotes that the i-th fuzzy rule, x _j (j = 1,2,…, m) are input variables and yi is an output. Furthermore, a _j i are the parameters contained in the consequent (then-part) of the i-th rule, and the A₁i,A₂i,…,A _m i are the linguistic values taken by the input variables in the antecedent (if-part) of the i-th rule. The meaning of these linguistic values is defined by corresponding membership functions. As shown in (1.1) and (1.2), this fuzzy model describes a nonlinear input-output relation.