Stability and robustness of fuzzy adaptive control of nonlinear systems

In this paper, we propose a new approach that guarantees the stability and robustness of an adaptive control law of a nonlinear system.The control diagram proposed contains a Takagi–Sugeno–Kang fuzzy controller (TSK-FC) and a training block allowing the online adaptation of the FC parameters. The adaptation algorithm used is based on the gradient with minimization of the quadratic error between the system output and that desired by using the direct method of Lyapunov. However, our approach considers the gradient step of each adaptive FC parameter to be bound. This approach was applied to the control of an inverted pendulum. The results obtained confirm well the validity of such an adaptation especially the guarantee of the pendulum stability and the robustness of its control with respect to the disturbances introduced on the FC parameters and the pendulum itself.