Backstepping design for unknown nonlinear delay systems using nonlinearly parameterized fuzzy approximator

A class of nonlinear delay systems with unknown dynamics is studied in this paper, and a controller is proposed by employing backstepping design method, which can make the output of the controlled system track the given reference signal. Fuzzy logic systems are used to approximate the unknown nonlinear functions in the design, and both the fuzzy weights and the parameters in the fuzzy basis functions are adjusted online by adaptive mechanism, so that the fuzzy basis functions do not need to be known beforehand. By choosing integrated Lyapunov functions, it is proved that the proposed controller can guarantee the closed-loop stability and the desired output tracking. Furthermore, simulation results demonstrate the correctness of the conclusion.