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Distributed formation control for fractional-order systems: dynamic interaction and absolute/relative damping. (English) Zbl 1222.93006
Summary: This paper studies the distributed formation control problem for multiple fractional-order systems under dynamic interaction with absolute/relative damping. In the context of this paper, formation control means that a group of systems reaches the desired state deviations via a local interaction. We first study a formation control algorithm in the case of a directed dynamic network topology. Convergence conditions on both the network topology and the fractional orders are presented. When the fractional-order $\alpha$ satisfies $\alpha \in (0,1)\cup (1+\frac 2 n)$, sufficient conditions on the network topology are given to ensure the formation control. Then we propose fractional-order formation control algorithms with absolute/relative damping and study the conditions on the network topology and the control gains such that the formation control will be achieved under a directed fixed network topology. The final equilibria are also given explicitly. Finally, several simulation examples are presented as a proof of concept.

##### MSC:
 93A14 Decentralized systems 93C15 Control systems governed by ODE 34A08 Fractional differential equations
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