A new design of Fuzzy Logic Controller based on generalized orthogonality principle

Improving Fuzzy Logic System (FLS) design is of main interest. Linguistic rules of a FLS can be converted into Fuzzy Basis Functions (FBFs). Moreover, numerical rules and their FBFs can be extracted from numerical training data. This combination of both linguistic and numerical information simultaneously makes the FBFs very useful. Since a specific FLS can be expressed as a linear combination of FBFs, we use generalized orthogonality principle on FBFs, that results in a better FLS. In this work, we consider each of these FBFs as a basis vector. We compute the optimal parameters of consequents that make the error vectors orthogonals to these FBFs, resulting in minimization of the magnitudes of these error vectors and consequently of the optimization of the FLS. This design method is used to tune the consequent parameters of a Fuzzy Logic Controller (FLC) for the non linear inverted pendulum on a cart. Simulation results show that a better control performance is achieved.