Adaptive fuzzy control for strict-feedback nonlinear time -delay systems without backstepping scheme

In this paper, an adaptive fuzzy tracking control is presented for a class of SISO nonlinear strict-feedback systems with unknown time delays. The proposed algorithm does not use the backstepping scheme rather it converts the strict-feedback time-delayed system to the normal form. The Mamdani-type fuzzy system is employed to approximate online the unknown lumped nonlinear function. The developed controller guarantees uniform ultimate boundedness of all signals in the closed-loop system. The designed control law is independent of the time delays and has a simple form with only one adaptive parameter vector, which is required to be updated on-line. As a result, the proposed control algorithm is considerably simpler than the previous ones based on backstepping. Simulation results are presented to verify the effectiveness of the proposed approach.