Feedback linearization adaptive fuzzy control for nonlinear systems: A multiple models approach

In this paper, the problem of controlling and stabilizing rapidly time-varying nonlinear unknown systems is being investigated. We propose a new scheme that incorporates Multiple Takagi-Sugeno (T-S) Identification Models into an indirect adaptive fuzzy technique. By using this approach, we increase the possibilities to produce a more accurate estimation at every step for the parameters of the unkown plant than in the case that only one identification model is used. One feedback linearization controller corresponds to each identification model, designed according to a pre-specified reference model. The controller to be applied is determined at every instant by the model which best approximates the plant. This is achieved by using a switching rule with a suitable performance index. Lyapunov stability theory is used in order to obtain the adaptive law for the multiple models parameters and to ensure the asymptotic stability of the system also. A modification in this adaptive law keeps the control input away from singularities. The effectiveness and the advantages of the proposed method are demonstrated by controlling an inverted pendulum with rapidly time-varying parameters.