Abstract
In this paper, the time-varying output formation-containment (TV-OFC) problem of homogeneous and heterogeneous descriptor fractional-order multi-agent systems (DFO-MASs) is investigated. The results obtained in previous works for nonsingular integer-order multi-agent systems can be regarded as particular cases of our results. This control aims at making leaders keep time-varying shape to move and followers move inside the convex hull spanned by leaders simultaneously. First, both the output feedback control strategy and observer-based control algorithm are designed to address the TV-OFC problem of heterogeneous DFO-MASs, where the virtual leader provides the reference trajectory for leaders to achieve the formation tracking. Then, sufficient conditions with less computation complexity are presented and the methods to determine gain matrices of the schemes are proposed for homogeneous and heterogeneous DFO-MASs, so as to achieve the TV-OFC. Finally, numerical examples are given to demonstrate the effectiveness of theoretical conclusions.
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