Robust adaptive multiple models based fuzzy control of nonlinear systems

A new robust adaptive multiple models based fuzzy control scheme for a class of unknown nonlinear systems is proposed in this paper. The nonlinear system is expressed by using the Takagi-Sugeno (T-S) method, and some identification adaptive T-S models along with their corresponding controllers, are used in order to control efficiently the unknown system. The modeling error that is produced due to the use of the T-S plant model can cause instability problems if it is not taken into account in the adaptation rules. In this paper, in order to solve this problem, we design a control scheme that is based on updating rules that utilize the ?-modification method. Every T-S controller is updated indirectly by using the robust updating rules and the final control signal is determined by using a performance index and a switching rule. By using the Lyapunov stability theory it is shown that ?-modification based rules can ensure the robustness of the system and define a bound for the steady state identification error. The main objectives of the robust controller are: (i) to ensure that the real plant system will remain stable despite the existence of modeling errors and (ii) to ensure that the real plant will track with a high accuracy the state trajectory of a given reference model. The effectiveness of the proposed method is demonstrated by computer simulations on a well known benchmark problem.