SCIENCE CHINA Information Sciences, Volume 60, Issue 9: 092203(2017) https://doi.org/10.1007/s11432-016-0498-8

## Structural controllability of multi-agent systems with absolute protocol underfixed and switching topologies

• AcceptedSep 29, 2016
• PublishedMay 19, 2017
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### Abstract

The paper investigates the structural controllability of leader-follower multi-agent systems underfixed and switching topologies. Three models of agents: double-integrator, high-orderintegrator and general-linear dynamics are analyzed. Necessary and sufficient graphical conditionsare provided for structural controllability based on communication topology of thesystem. In particular, a linear neighbor-based control protocol is designed for generic linearagents under which structural controllability is proved to be uniquely determined bycommunication topology structure. The role that leaders play in the structural controllabilityof multi-agent system is characterized, and a method is developed to realize structural controllabilityunder single leader. The results clearly indicate the role of leaders and theeffect of communication topology on structural controllability.

### Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61375120, 61533001, 61603288).

• Figure 1

(Color online) A communication topology, where agents 1 and 2 are leaders.

• Figure 2

(Color online) A diamond configuration. The circle and asterisk denote the initial state and the final desired configuration, respectively.

• Figure 3

(Color online) Switching topology with two subgraphs. (a) The subgraph $\mathcal{G}_{1}$; (b) the subgraph $\mathcal{G}_{2}$; (c) the union graph $\tilde{\mathcal{G} }$ of $\mathcal{G}_{1}$ and $\mathcal{G}_{2}$.

• Figure 4

(Color online) A triangle configuration. The circle and asterisk denote the initial state and the final desired configuration, respectively.

• Figure 5

(Color online) (a) Three disjoint leader-follower connected graphs $\mathcal{G}_{1}, \mathcal{G}_{2}$ and $\mathcal{G}_{3}$; (b) the constructed graph $\bar{\mathcal{G} }$.

• Figure 6

(Color online) (a) The original graph $\mathcal{G}$; (b) all strongly connected components of $\mathcal{G}$; (c) the single leader structurally controllable topology.

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