Adaptive switching control of fuzzy dynamical systems based on hybrid T-S multiple models

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.