Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients

Abstract—In this paper, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time de-lays. The proposed design method does not require a priori knowl-edge of the signs of the unknown virtual control coefficients. The unknown time delays are compensated for using appropriate Lya-punov–Krasovskii functionals in the design. It is proved that the proposed backstepping design method is able to guarantee semi-global uniformly ultimately boundedness of all the signals in the closed-loop. In addition, the output of the system is proven to con-verge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach. Index Terms—Adaptive control, neural networks, nonlinear time-delay systems