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Zbl 1222.93006
Cao, Yongcan; Ren, Wei
Distributed formation control for fractional-order systems: dynamic interaction and absolute/relative damping. (English)
[J] Syst. Control Lett. 59, No. 3-4, 233-240 (2010). ISSN 0167-6911

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 2000:: *93A14 Decentralized systems
93C15 Control systems governed by ODE
34A08

Keywords: cooperative control; distributed algorithms; fractional-order systems; coordination

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Zentralblatt MATH Berlin [Germany]