Adaptive control of nonlinear systems with unmodeled dynamics and time-varying state delays

Based on backstepping design, a novel adaptive control scheme is proposed for a class of nonlinear strict feedback systems with unmodeled dynamics and unknown time-varying delays. The neural networks are used to approximate the unknown continuous functions. An available dynamic signal is introduced to dominate the unmodeled dynamics. The unknown time-varying delays can be compensated for using appropriate Lyapunov-Krasovskii functional. Compared with the existing results, system model proposed in this paper is more general, the restriction of the dynamic disturbance is relaxed, and the number of online adjusted parameters and the complexity of the design are both reduced. By theoretical analysis, the closed-loop system is proved to be semi-global uniformly ultimately bounded.