Uncertain fractional grey model analysis with optimal H-infinite control

Model inaccuracies or parameter uncertainties are unavoidable in the practical control systems, while the uncertain properties could be modeled and estimated by the grey system. Among many grey models, fractional grey model is recently proposed and popularly used in many model analysis and prediction problems. In this paper, the structure uncertainties and external disturbances are considered using the fractional grey model for control problem. When the model of the fractional grey controlled object and its parameters range is known, based on the model properties, it can be also approximated by a high order one, then the satisfactory adaptive ability and robustness can be obtained by the H-infinite optimal control. In the numerical simulation part, the corresponding results demonstrate the effectiveness of the robust fractional grey control algorithm, and it can be used for other grey control and related problems.