adaptive fuzzy tracking control for a class of nonlinear systems with unknown distributed time-varying delays and unknown control directions

in this paper, an adaptive fuzzy control scheme is proposed for a class of perturbed strict-feedback nonlinear systems with unknown discrete and distributed time-varying delays, and the proposed design method does not require a priori knowledge of the signs of the control gains.based on the backstepping technique, the adaptive fuzzy controller is constructed. the main contributions of the paper are that (i) by constructing appropriate lyapunov functionals and using the nussbaum functions, the adaptive tracking control problem is solved for the strict-feedback unknown nonlinear systems with the unknown discrete and distributed time-varying delays and the unknown control directions (ii) the number of adaptive parameters is independent of the number of rules of fuzzy logic systems and system state variables, which reduces the computation burden greatly. it is proven that the proposed controller guaranteesthat all the signals in the closed-loop system are bounded and the system output converges to a small neighborhood of the desired reference signal. finally, an example is used to show the effectiveness of theproposed approach.