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Identification and control of dynamical systems based on cause-effect fuzzy models

An incremental type of dynamical system model, based on cause-effect relationships is proposed. It is a fuzzy-like model where the relationships between the change-of-past-inputs and change-of-the-output is represented by a fuzzy membership function. The shape of the membership function directly affects the type of the modeled dynamics. Three identification schemes using the least mean squares algorithm and its modifications are discussed and analyzed as follows: direct identification, reduced size indirect identification, and the newly proposed soft-guided identification. The indirect identification is achieved by tuning a simple one-dimensional Takagi-Sugeno model that represents in an indirect way the cause-effect relations in the dynamical system. The soft guided identification uses a human specified reference model and makes a kind of compromise solution between the pure data fitting and pure model fitting.