Grey differential system and control problems based on the fractional calculus

The fractional-order has been studied as an alternative calculus in mathematics and many dynamical systems can be described by its differential equations. Grey theory is used to process the system when the information is partly known or the data samples are incomplete. Therefore, combining the advantage of grey and the fractional system will become a strong tool to estimate the real world. The purpose of this paper is to develop fractional-order grey mathematical models based on the operation properties of fractional calculus and grey numbers. The general Linear Time Invariant (LTI) system with fractional and grey numbers was given. The simulation results illustrated that fractional-order grey system could better depict the system, which will be widely used in the control theory and related field.

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