Polynomial Fuzzy Models for Nonlinear Control: A Taylor Series Approach

Classical Takagi–Sugeno (T–S) fuzzy models are formed by convex combinations of linear consequent local models. Such fuzzy models can be obtained from nonlinear first-principle equations by the well-known sector-nonlinearity modeling technique. This paper extends the sector-nonlinearity approach to the polynomial case. This way, generalized polynomial fuzzy models are obtained. The new class of models is polynomial, both in the membership functions and in the consequent models. Importantly, T–S models become a particular case of the proposed technique. Recent possibilities for stability analysis and controller synthesis are also discussed. A set of examples shows that polynomial modeling is able to reduce conservativeness with respect to standard T–S approaches as the degrees of the involved polynomials increase.