H∞ tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach

A fuzzy logic controller equipped with a training (adaptive) algorithm is proposed in this work to achieve H^∞ tracking performance for a class of uncertain (model free) nonlinear single-input single-output (SISO) systems with external disturbances. An attempt is also made to create a bridge between two important control design techniques, i.e., H^∞ control design and fuzzy control design, so as to supply H^∞ control design with more intelligence and fuzzy control design with better performance. The perfect matching of parameters in an adaptive fuzzy logic system is generally deemed impossible. Therefore, a desired tracking performance cannot be guaranteed in the conventional adaptive fuzzy control systems. In this study, the influence of both fuzzy logic approximation error and external disturbance on the tracking error is attenuated to a prescribed level. Both indirect and direct adaptive fuzzy controllers are employed to treat this H^∞ tracking problem. The authors´ results indicate that arbitrarily small attenuation level can be achieved via the proposed adaptive fuzzy control algorithm if a weighting factor of control variable is adequately chosen. The proposed design method is also useful for the robust tracking control design of the nonlinear systems with external disturbances and a large uncertainty or unknown variation in plant parameters and structures. Furthermore, only smooth control signals are needed via the proposed control designs. Two simulation examples are given finally to illustrate the performance of the proposed methods. Computer simulation results confirm that the effect of both the fuzzy approximation error and external disturbance on the tracking error can be attenuated efficiently by the proposed method