CLC number: TP13
On-line Access: 2015-10-08
Received: 2015-03-07
Revision Accepted: 2015-07-28
Crosschecked: 2015-08-25
Cited: 0
Clicked: 6787
Di Guo, Rong-hao Zheng, Zhi-yun Lin, Gang-feng Yan. Controllability analysis of second-order multi-agent systems with directed and weighted interconnection[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(10): 838-847.
@article{title="Controllability analysis of second-order multi-agent systems with directed and weighted interconnection",
author="Di Guo, Rong-hao Zheng, Zhi-yun Lin, Gang-feng Yan",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="16",
number="10",
pages="838-847",
year="2015",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1500069"
}
%0 Journal Article
%T Controllability analysis of second-order multi-agent systems with directed and weighted interconnection
%A Di Guo
%A Rong-hao Zheng
%A Zhi-yun Lin
%A Gang-feng Yan
%J Frontiers of Information Technology & Electronic Engineering
%V 16
%N 10
%P 838-847
%@ 2095-9184
%D 2015
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1500069
TY - JOUR
T1 - Controllability analysis of second-order multi-agent systems with directed and weighted interconnection
A1 - Di Guo
A1 - Rong-hao Zheng
A1 - Zhi-yun Lin
A1 - Gang-feng Yan
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 16
IS - 10
SP - 838
EP - 847
%@ 2095-9184
Y1 - 2015
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/FITEE.1500069
Abstract: This article investigates the controllability problem of multi-agent systems. Each agent is assumed to be governed by a second-order consensus control law corresponding to a directed and weighted graph. Two types of topology are considered. The first is concerned with directed trees, which represent the class of topology with minimum information exchange among all controllable topologies. A very simple necessary and sufficient condition regarding the weighting scheme is obtained for the controllability of double integrator multi-agent systems in this scenario. The second is concerned with a more general graph that can be reduced to a directed tree by contracting a cluster of nodes to a component. A similar necessary and sufficient condition is derived. Finally, several illustrative examples are provided to demonstrate the theoretical analysis results.
This paper proposes a method to choose weights in a directed graph that models a leader-follower network of double integrators so that the network is controllable. The proposed condition which basically consists in choosing different weights for each link is proven to be necessary and sufficient. The authors also consider contracted-trees, which slightly generalize the result to graphs in which nodes can clustered so that a directed tree connects the clusters and inside the clusters there can be arbitrary feedback links among nodes of the same cluster. The paper is well written and clear. The results seem technically sound.
[1]Antsaklis, P.J., Michel, A.N., 2006. Linear Systems. Birkhäuser, Boston, USA.
[2]Borsche, T., Attia, S.A., 2010. On leader election in multi-agent control systems. Proc. Chinese Control and Decision Conf., p.102-107.
[3]Cai, N., Cao, J., Liu, M., et al., 2014. On controllability problems of high-order dynamical multi-agent systems. Arab. J. Sci. Eng., 39(5):4261-4267.
[4]de la Croix, J.P., Egerstedt, M.B., 2012. Controllability characterizations of leader-based swarm interactions. Proc. AAAI Symp. on Human Control of Bio-inspired Swarms, p.1-6.
[5]Franceschelli, M., Gasparri, A., Giua, A., et al., 2009. Decentralized Laplacian eigenvalues estimation for networked multi-agent systems. Proc. 48th IEEE Conf. on Decision and Control, Jointly with 28th Chinese Control Conf., p.2717-2722.
[6]Franceschelli, M., Martini, S., Egerstedt, M., et al., 2010. Observability and controllability verification in multi-agent systems through decentralized Laplacian spectrum estimation. Proc. 49th IEEE Conf. on Decision and Control, p.5775-5780.
[7]Han, Z., Lin, Z., Fu, M., et al., 2015. Distributed coordination in multi-agent systems: a graph Laplacian perspective. Front. Inform. Technol. Electron. Eng., 16(6):429-448.
[8]Ji, Z., Wang, Z., Lin, H., et al., 2010. Controllability of multi-agent systems with time-delay in state and switching topology. Int. J. Contr., 83(2):371-386.
[9]Ji, Z., Lin, H., Yu, H., 2012. Leaders in multi-agent controllability under consensus algorithm and tree topology. Syst. Contr. Lett., 61(9):918-925.
[10]Jiang, F., Wang, L., Xie, G., et al., 2009. On the controllability of multiple dynamic agents with fixed topology. Proc. American Control Conf., p.5665-5670.
[11]Lin, C.T., 1974. Structural controllability. IEEE Trans. Autom. Contr., 19(3):201-208.
[12]Lin, Z., Ding, W., Yan, G., et al., 2013. Leader-follower formation via complex Laplacian. Automatica, 49(6):1900-1906.
[13]Lin, Z., Wang, L., Han, Z., et al., 2014. Distributed formation control of multi-agent systems using complex Laplacian. IEEE Trans. Autom. Contr., 59(7):1765-1777.
[14]Liu, B., Chu, T., Wang, L., et al., 2008. Controllability of a leader-follower dynamic network with switching topology. IEEE Trans. Autom. Contr., 53(4):1009-1013.
[15]Liu, B., Su, H., Li, R., et al., 2014. Switching controllability of discrete-time multi-agent systems with multiple leaders and time-delays. Appl. Math. Comput., 228:571-588.
[16]Liu, X., Lin, H., Chen, B., 2013. Graph-theoretic characterisations of structural controllability for multi-agent system with switching topology. Int. J. Contr., 86(2):222-231.
[17]Liu, Y., Slotine, J.J., Barabási, A.L., 2011. Controllability of complex networks. Nature, 473:167-173.
[18]Lou, Y., Hong, Y., 2012. Controllability analysis of multi-agent systems with directed and weighted interconnection. Int. J. Contr., 85(10):1486-1496.
[19]Martini, S., Egerstedt, M., Bicchi, A., 2010. Controllability analysis of networked systems using equitable partitions. Int. J. Syst. Contr. Commun., 2(1-2):100-121.
[20]Sundaram, S., Hadjicostis, C.N., 2013. Structural controllability and observability of linear systems over finite fields with applications to multi-agent systems. IEEE Trans. Autom. Contr., 58(1):60-73.
[21]Tanner, H.G., 2004. On the controllability of nearest neighbor interconnections. Proc. 43rd IEEE Conf. on Decision and Control, p.2467-2472.
[22]Twu, P., Egerstedt, M., Martini, S., 2010. Controllability of homogeneous single-leader networks. Proc. 49th IEEE Conf. on Decision and Control, p.5869-5874.
[23]Zheng, R., Lin, Z., Fu, M., et al., 2015. Distributed control for uniform circumnavigation of ring-coupled unicycles. Automatica, 53:23-29.
Open peer comments: Debate/Discuss/Question/Opinion
<1>