Fuzzy-based Higher Adaptive Order Sliding Mode Observers

In this article, I introduce the notion of Fuzzy-based Higher adaptive order sliding mode observers through the example of the super-twisting adaptive order sliding mode observer. I begin by presenting the super-twisting second order sliding mode observer for systems in triangular form. Then I replace the sign functions with fuzzy inference systems in order to eliminate the chattering effect. I then show that this variant of the super-twisting second order sliding mode observer may not converge depending on the input, so I replace the square root with an adaptive power $\gamma$. The efficiency of the proposed method is illustrated by simulations made on MATLAB/Simulink.