Adaptive neural control of state delayed non-linear systems with unmodelled dynamics and distributed time-varying delays

In this study, a robust adaptive control is proposed for a class of strict-feedback state delayed non-linear systems with unmodelled dynamics and distributed time-varying delays using radial basis function neural networks. Dynamic uncertainties are dealt with using separation technique and introducing a dynamic signal. The terms including state time-varying delay and distributed time-varying delay uncertainties are compensated for by constructing appropriate Lyapunov–Krasovskii functionals. Using Young's inequality, only one learning parameter need to be tuned online at each step of recursion. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness of all signals in the closed-loop system. Simulation results demonstrate the effectiveness of the proposed approach.

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