Distributed formation control for fractional-order systems: Dynamic interaction and absolute/relative damping

This paper studies the distributed formation control problem for multiple fractional-order systems under dynamic interaction and 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. The convergence conditions on both the network topology and the fractional orders are presented. When the fractional-order αα satisfies α∈(0,1)⋃(1+2n), sufficient conditions on the network topology are given to ensure the formation control. We then 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.