A robust adaptive fuzzy wavelet network based controller for a class of non-linear systems

This paper deals with the synthesis of an adaptive fuzzy wavelet network (FWN) controller for an nth order multi input multi output (MIMO) non-linear system suffering from parameters uncertainties and subjected to external perturbation. The proposed approach allows combining the advantages of the fuzzy logic system and those of wavelet networks to approximate quickly the unknown system dynamics with neither a prior knowledge about such dynamics nor offline learning phase. The FWN is adjusted online using some adaptation laws deduced from the stability analysis which guarantees a non-singular control action. Furthermore, the robustness of the proposed method is improved such that the knowledge of the upper bounds of both the external disturbances and the approximation errors is not required. Moreover, a variable sliding mode control (VSMC) technique is proposed to reduce the starting energy, caused by the presence of approximations errors and external disturbances, without deteriorating the tracking performances. To ensure the robustness of the overall closed loop system, analytical demonstration using Lyapunov theorem is considered. Finally, a numerical example is presented to validate our approach and to show the fast convergence, good tracking and the robustness of the closed loop system.