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This paper proposes an adaptive neural network (NN) tracking controller for a class of multi-input multi-output (MIMO) nonlinear systems with unknown delays. Using a separation technique, the requirement for special assumptions on the bounds of the delay functional is removed, thereby extending the applicability of the results to a larger class of systems. To deal with uncertain or unknown functions in the system dynamics, including the unknown bounds of the delay functional, NNs are utilized to estimate and compensate for them. Using Lyapunov-Krasovskii functional and adaptive NN backstepping, it is shown that the proposed controller guarantees all signals to be semi-globally uniformly ultimately bounded (SGUUB) while the outputs track specified desired trajectories.