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A new hybrid scheme which contains multiple fixed and adaptive Takagi-Sugeno (T-S) identification models is proposed in this paper in order to control efficiently a class of unknown nonlinear dynamical fuzzy systems. One state feedback fuzzy controller corresponds to each T-S model, producing its signal according to the certainty equivalence approach. A performance index and an appropriate switching rule are used to determine the T-S model which best approximates the plant and consequently to pick the best available controller at every time instant. There are two kind of adaptive models: one free running adaptive model and one reinitialized adaptive model which uses the parameters of the best fixed model at every time instant. Lyapunov stability theory is used in order to obtain the adaptive law for every adaptive model's parameters ensuring the asymptotic stability of the system. Singularity problems in the control signal are avoided by modifying the adaptive law and the Next Best Controller Logic (NBCL) ensures the controller's feasibility. A computer simulation example is given to verify the theoretical results.

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A new fuzzy control architecture for unknown nonlinear systems in the framework of multiple models control is proposed in this paper. The architecture incorporates different kinds of identification models and controllers offering enhanced overall performance. More specifically, the fixed models which are widely used in multiple models control are becoming more flexible and they end up to be semi-fixed models. When semi-fixed models are combined with a free adaptive model and a reinitialized adaptive model, the result is very promising and offers many advantages in comparison with former control methods. All these models are represented by using the Takagi-Sugeno (T-S) method which is very useful for representing unknown or partially unknown nonlinear systems. The identification T-S models define the control signal at every time instant by updating their own state feedback fuzzy controllers and 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 semi-fixed models are updated according to a rule which leads the models towards a direction that minimizes the performance index. 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 over other methods are illustrated by computer simulations.