Energy scaling and reduction in controlling complex networks

Royal Society Open Science

Volumn 3, Issue 4, 2016, Pages

  Chen, Yu Zhong ^a   Wang, Le Zhi ^a   Wang, Wen Xu ^b   Lai, Ying Cheng ^a  

^a Arizona State University   (United States)

^b BEIJING NORMAL UNIVERSITY   (China)

Author keywords

Complex networks; Control; Scaling law

Indexed keywords

EID: 84964300665     PISSN: None     EISSN: 20545703     Source Type: Journal    
DOI: 10.1098/rsos.160064     Document Type: Article

References (34)

1. Strogatz SH. 2001 Exploring complex networks. Nature 410, 268–276. (doi:10.1038/35065725)
2. Albert R, Barabási AL. 2002 Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97. (doi:10.1103/RevModPhys.74.47)
3. Mendes JFF, Dorogovtsev SN, Ioffe AF. 2003 Evolution of networks: from biological nets to the internet and theWWW, 1st edn. Oxford UK: Oxford University Press.
4. Pastor-Satorras R, Vespignani A. 2004 Evolution and structure of the internet: a statistical physics approach, 1st edn. Cambridge UK: Cambridge University Press.
5. Barrat A, Barthélemy M, Vespignani A. 2008 Dynamical processes on complex networks, 1st edn. Cambridge UK: Cambridge University Press.
6. Newman MEJ. 2010 Networks: an introduction, 1st edn. Oxford, UK: Oxford University Press.
7. Lombardi A, Hörnquist M. 2007 Controllability analysis of networks. Phys. Rev. E 75, 056110. (doi:10.1103/PhysRevE.75.056110)
8. Liu B, Chu T, Wang L, Xie G. 2008 Controllability of a leader-follower dynamic network with switching topology. IEEE Trans. Automat. Contr. 53, 1009–1013. (doi:10.1109/TAC.2008.919548)
9. Rahmani A, Ji M, Mesbahi M, Egerstedt M. 2009 Controllability of multi-agent systems from a graph-theoretic perspective. SIAM J. Contr. Optim. 48, 162–186. (doi:10.1137/060674909)
10. Liu YY, Slotine JJ, Barabási AL. 2011 Controllability of complex networks. Nature 473, 167–173. (doi:10.1038/nature10011)
11. Wang WX, Ni X, Lai YC, Grebogi C. 2011 Optimizing controllability of complex networks by small structural perturbations. Phys. Rev. E 85, 026115. (doi:10.1103/PhysRevE.85.026115)
12. Nacher JC, Akutsu T. 2012 Dominating scale-free networks with variable scaling exponent: heterogeneous networks are not difficult to control. New J. Phys. 14, 073005. (doi:10.1088/1367-2630/14/7/073005)
13. Yan G, Ren J, Lai YC, Lai CH, Li B. 2012 Controlling complex networks: How much energy is needed? Phys. Rev. Lett. 108, 218703. (doi:10.1103/PhysRevLett.108.218703)
14. Nepusz T, Vicsek T. 2012 Controlling edge dynamics in complex networks. Nat. Phys. 8, 568–573. (doi:10.1038/nphys2327)
15. Liu YY, Slotine JJ, Barabási AL. 2013 Observability of complex systems. Proc. Natl Acad. Sci. USA 110, 2460–2465. (doi:10.1073/pnas.1215508110)
16. Yuan ZZ, Zhao C, Di ZR, Wang WX, Lai YC. 2013 Exact controllability of complex networks. Nat. Commun. 4, 2447. (doi:10.1038/ncomms3447)
17. Menichetti G, Dall’Asta L, Bianconi G. 2014 Network controllability is determined by the density of low in-degree and out-degree nodes. Phys. Rev. Lett. 113, 078701. (doi:10.1103/PhysRevLett.113.078701)
18. Ruths J, Ruths D. 2014 Control profiles of complex networks. Science 343, 1373–1376. (doi:10.1126/science.1242063)
19. Wuchty S. 2014 Controllability in protein interaction networks. Proc. Natl Acad. Sci. USA 111, 7156–7160. (doi:10.1073/pnas.1311231111)
20. Yuan ZZ, Zhao C, Wang WX, Di ZR, Lai YC. 2014 Exact controllability of multiplex networks. New J. Phys. 16, 103036. (doi:10.1088/1367-2630/16/10/103036)
21. Whalen AJ, Brennan SN, Sauer TD, Schiff SJ. 2015 Observability and controllability of nonlinear networks: the role of symmetry. Phys. Rev. X 5, 011005. (doi:10.1103/PhysRevX.5.011005)
22. Yan G, Tsekenis G, Barzel B, Slotine JJ, Liu YY, Barabási AL. 2015 Spectrum of controlling and observing complex networks. Nat. Phys. 11, 779–786. (doi:10.1038/nphys3422)
23. Chen YZ, Wang LZ, Wang WX, Lai YC. 2015 The paradox of controlling complex networks: control inputs versus energy requirement. (http://arxiv.org/abs/1509.03196v1)
24. Lin CT. 1974 Structural controllability. IEEE Trans. Automat. Contr. 19, 201–208. (doi:10.1109/TAC.19741100557)
25. Hopcroft JE, Karp RM. 1973 An n5/2 algorithm for maximum matchings in bipartite graphs. SIAM J. Comput. 2, 225–231. (doi:10.1137/0202019)
26. Zhou H, Ou-Yang ZC. 2003 Maximum matching on random graphs. (http://arxiv.org/abs/cond-mat/0309348)
27. Zdeborová L, Mézard M. 2006 The number of matchings in random graphs. J. Stat. Mech. 2006, P05003. (doi:10.1088/1742-5468/2006/05/P05003)
28. Hautus MLJ. 1969 Controllability and observability conditions of linear autonomous systems. In Nederlandse Academie vanWetenschappen. Series A: Mathematical Sciences, vol. 72, pp. 443–448. Amsterdam, The Netherlands: Elsevier.
29. Rugh WJ. 1996 Linear systems theory. Englewood Cliffs, NJ: Prentice-Hall, Inc.
30. Erdős P, Rényi A. 1959 On random graphs, I. Publ. Math. 6, 290–297
31. Erdős P, Rényi A. 1960 On the evolution of random graphs. Publ. Math. Inst. Hung. Acad. Sci. 5, 17–61
32. Sorrentino F, di Bernardo M, Garofalo F, Chen G. 2007 Controllability of complex networks via pinning. Phys. Rev. E 75, 046103. (doi:10.1103/PhysRevE.75.046103)
33. Lai YC. 2014 Controlling complex, nonlinear dynamical networks. Nat. Sci. Rev. 1, 339–341. (doi:10.1093/nsr/nwu023)
34. Pasqualetti F, Zampieri S. 2014 On the controllability of isotropic and anisotropic networks. In 53rd IEEE Conf. on Decision and Control, pp. 607–612. Los Angeles, CA: IEEE.