Adaptive control of nonlinear systems with time delays via backstepping method

In this paper, the adaptive control problem is investigated for a class of strict-feedback nonlinear time-delay systems with triangular structure. Via the backstepping method, new Lyapunov-Krasovskii functionals are constructed in the designing process of the control input of each subsystem. This eliminates the time-delay terms without introducing any uncertainties to the system. Finally, an adaptive tracking controller has been constructed and all the signals in the closed-loop system are bounded. Simulation results are provided to show the effectiveness of the proposed approach.