Controllability analysis of second-ordermulti-agent systemswith directed andweighted interconnection

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.

Keywords

Multi-agent systems / Controllability / Directed tree

References

[1] Antsaklis, P.J., Michel, A.N., 2006. Linear Systems. Birkhäuser, Boston, USA. [

[2] Borsche, T., Attia, S.A., 2010. On leader election in multiagent control systems. Proc. Chinese Control and Decision Conf., p.102−107. [

[3] Cai, N., Cao, J., Liu, M., , 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., , 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., , 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., , 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., , 2010. Controllability of multiagent 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., , 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., , 2013. Leader-follower formation via complex Laplacian. Automatica, 49(6): 1900−1906. [

[13] Lin, Z., Wang, L., Han, Z., , 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., , 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., , 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 multiagent 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., , 2015. Distributed control for uniform circumnavigation of ring-coupled unicycles. Automatica, 53: 23−29. [