This paper deals with a nonlinear adaptive control design based on synergetic control, which also uses fuzzy systems to approximate the dynamics of nonlinear systems. The stability of the closed-loop system is ensured by the Lyapunov synthesis in the sense that all the signals are bounded, and the controller parameters adjusted by adaptation laws. The proposed algorithm is applied to an inverted pendulum to track a sinusoidal reference trajectory. Simulations and discussion are presented to illustrate the new robust adaptive fuzzy synergetic control described in this work.

In this paper, we are interested in the adaptive fuzzy control a technique has been studied and applied, namely adaptive fuzzy control based on theory of Lyapunov. The system based on the stability theory is used to approximate the gains ke and kdce to ensure the stability of the control in particular time, simulations results obtained by using MATLAB environment gives that the fuzzy adaptive control more robust, also it has superior dynamics performances. The results and test of robustness will be presented.