Adaptive composite dynamic surface neural control for nonlinear fractional-order systems subject to delayed input

In the article, the adaptive composite dynamic surface neural controller design problem for nonlinear fractional-order systems (NFOSs) subject to delayed input is discussed. A fractional-order auxiliary system is first designed to solve the input-delay problem. By using the developed novel estimation models, the defined prediction errors and the states of error system can decide the weights of radial basis function neural networks (RBFNNs). During the dynamic surface controller design process, the developed fractional-order filters are designed to handle the complexity explosion problem when the classical backstepping control technique is utilized. It is shown that the designed adaptive composite neural controller ensures that all the system state variables are bounded and the tracking error of the considered system finally tends to a small neighborhood of zero. Finally, the results of the simulation explain the feasibility of the developed controller. In addition, the developed controller can also be applied to single input and single output(SISO) nonlinear systems subject to a unitary input function.