Improving the performance of multiple models fuzzy control by using semi-fixed and adaptive models

The role of the fixed models that participate in a hybrid switching control scheme is investigated in this paper. The control scheme is based on some semi-fixed and adaptive Takagi-Sugeno (T-S) identification models and its main target is to control efficiently a class of unknown nonlinear dynamical fuzzy systems. These identification models define the control signal at every time instant with their own state feedback fuzzy controllers which are parameterized by using the certainty equivalence approach. A performance index and an appropriate switching rule are used to determine the T-S model that approximates the plant best and consequently to pick the best available controller at every time instant. The identification models bank consists of three kind of models: i. a number of semi-fixed T-S models which are redistributed during the control procedure, ii. a free adaptive T-S model which is randomly initialized and iii. a reinitialized adaptive model which uses the parameters of the best semi-fixed model at every time instant. The combination of these different model categories, offers many advantages to the control scheme. The asymptotic stability of the system and the adaptive laws for the adaptive models are given by using Lyapunov stability theory. The effectiveness and the advantages of the proposed method are illustrated by some computer simulations.