Controllability of multi-agent systems is determined by the interconnection topologies. In practice, losing agents can change the topologies of multi-agent systems, which may affect the controllability. In order to preserve controllability, this paper first introduces the concept of non-fragility of controllability. In virtue of the notion of cutsets, necessary and sufficient conditions are established from a graphic perspective, for almost surely strongly/weakly preserving controllability, respectively. Then, the problem of leader selection to preserve controllability is proposed. The tight bounds of the fewest leaders to achieve strongly preserving controllability are estimated in terms of the diameter of the interconnection topology, and the cardinality of the node set. Correspondingly, the tight bounds of the fewest leaders to achieve weakly preserving controllability are estimated in terms of the cutsets of the interconnection topology. Furthermore, two algorithms are established for selecting the fewest leaders to strongly/weakly preserve the controllability. In addition, the algorithm for leaders’ locations to maximize non-fragility is also designed. Simulation examples are provided to illuminate the theoretical results and exhibits how the algorithms proceed.
non-fragility controllability preserving cutset leader selection almost surely
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This work was supported by National Natural Science Foundation of China (Grant Nos. 61375120, 61603288).
Zhang Z, Zhang L, Hao F, et al. Leader-following consensus for linear and lipschitz nonlinear multiagent systems with quantized communication. IEEE Trans Cyber, 2016, 47: 1970–1982CrossRefGoogle Scholar
Jing G, Zheng Y, Wang L. Consensus of multiagent systems with distance-dependent communication networks. IEEE Trans Neural Netw Learn Syst, 2017, 28: 2712–2726CrossRefGoogle Scholar
Notarstefano G, Parlangeli G. Controllability and observability of grid graphs via reduction and symmetries. IEEE Trans Autom Control, 2013, 58: 1719–1731MathSciNetCrossRefzbMATHGoogle Scholar
Partovi A, Lin H, Ji Z. Structural controllability of high order dynamic multi-agent systems. In: Proceedings of IEEE Conference on Robotics Automation and Mechatronics, Singapore, 2010. 327–332Google Scholar
Zamani M, Lin H. Structural controllability of multi-agent systems. In: Proceedings of the 2009 American Control Conference, St. Louis, 2009. 5743–5748CrossRefGoogle Scholar
Goldin D, Raisch J. On the weight controllability of consensus algorithms. In: Proceedings of European Control Conference, Zurich, 2013. 233–238Google Scholar
Jafari S, Ajorlou A, Aghdam A G. Leader selection in multi-agent systems subject to partial failure. In: Proceedings of the 2011 American Control Conference, San Francisco, 2011. 5330–5335CrossRefGoogle Scholar