Contribution à la commande moderne des systèmes non linéaires multivariables non affines

Abstract

Adaptive fuzzy sliding mode control can be defined as a method of robust control, in which fuzzy systems are used to approximate unknown functions, some of the system parameters are adapted online to ensure the stability of the closed loop system and, uncertainties and external disturbances are compensated by the sliding mode. In this thesis, two adaptive fuzzy approaches are proposed to control some classes of nonlinear non-affine SISO and MIMO systems. For SISO systems, the proposed control contains three terms, the first stabilize the linearized dynamic system, the second uses the implicit function theorem and a fuzzy system to approximate an unknown nonlinear function and the last term ensures the robustness of control. For the class of MIMO systems, an unknown ideal controller, whose existence is shown by the global implicit function theorem, is approximated by Takagi- Suegeno fuzzy systems with a constant conclusion. This approach ensures the robustness of the control via sliding mode term. The adaptation laws in both approaches are derived by analyzing the stability of the closed loop system by Lyapunov synthesis.