Recent progress in controllability of complex network

Hou Lü-Lin; Lao Song-Yang; Xiao Yan-Dong; Bai Liang

doi:10.7498/aps.64.188901

Abstract

The model, structure and dynamics of complex systems and networks are studied to control complex systems, which reflects the ability to understanding complex systems. Recently, the research on controllability of complex networks by using control theory and complexity science has attracted much attention. It has been investigated extensively by many scientists from various fields, and many meaningful achievements have been obtained in the past few years. In this paper, the process of controllability of complex networks is discussed, the framework of structural controllability based on maximum matching is introduced in detail, and the relevant research status since 2011 is summarized. Controllabilities of complex networks are introduced in the following aspects: different types of controllabilities, relationship between controllability and network statistical characteristics, classification and measures based on controllability, robustness of controllability, and optimization methods of controllability. Finally, the questions urgent to solve in controllability are discussed, so as to give a help to the the study in this respect.#br#There are five sections in this paper, which involve with different aspects of controllability. In the introduction section, the research work of controllability since 2011 is briefly mentioned, and the difference between controllability and previous pinning controllability is clarified. In the second section, the concept of controllability and different types of controllabilities are discussed in detail, including structural controllability, exact controllability, controllability with edge dynamics and controllability with nodal dynamics. In the third section, the relationship between controllability and network structure is investigated, especially the effects of common statistical characteristics and low-degree nodes on controllability. In the fourth section, the measures based on controllability are introduced, which includes control profiles, control range, control centrality, control capacity and control modality. In the fifth section, the research work about control robustness is discussed from robustness measures to optimization methods. In the fifth section, the optimization methods of controllability are introduced, which are classified into two different strategies: topology and edge direction.

Keywords:

Authors and contacts

1.
Science and Technology on Information Systems Enginering Laboratory, National University of Defense Technology, Changsha 410073, China;
2.
School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia

Corresponding author: Hou Lü-Lin, houlvlin@gmail.com

References

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[3]	Lombardi A, Hörnquist M 2007 Phys. Rev. E 75 056110
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[32]	Hou L L, Small M, Lao S Y 2014 Phys. Lett. A 378 3426
[33]	Ruths J, Ruths D 2014 Science 343 1373
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[35]	Wang B B, Gao L, Gao Y 2012 J. Stat. Mech. 2012 P04011
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[46]	Shargel B, Sayama H, Epstein I R, Bar-Yam Y 2003 Phys. Rev. Lett. 90 068701
[47]	Pu C L, Pei W J, Michaelson A 2012 Physica A 391 4420
[48]	Nie S, Wang X, Zhang H, Li Q, Wang B 2014 PLoS One 9 e89066
[49]	Wang B, Gao L, Gao Y, Deng Y 2013 EPL 101 58003
[50]	Xiao Y D, Lao S Y, Hou L L, Bai L 2014 Chin. Phys. B 23 118902
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[53]	Ruths J, Ruths D 2013 Complex Networks IV (New York: Springer) 476 185
[54]	Wang W X, Ni X, Lai Y C, Grebogi C 2012 Phys. Rev. E 85 026115
[55]	Hou L L, Lao S Y, Bu J, Bai L 2013 International Conference on Intelligent System Design and Engineering Applications 709
[56]	Hou L L, Lao S Y, Liu G, Bai L 2012 Chin. Phys. Lett. 29 108901
[57]	Xiao Y D, Lao SY, Hou L L, Bai L 2014 Phys. Rev. E 90 042804
[58]	Ding J, Lu Y Z, Chu J 2013 Physica A 392 6603
[59]	Yan G, Ren J, Lai Y C, Lai C H, Li B W 2012 Phys. Rev. Lett. 108 218703
[60]	Delpini D, Battiston S, Riccaboni M, Gabbi G, Pammolli F, Caldarelli G 2013 Sci. Rep. 3 1626
[61]	Wuchty S 2014 Proc. Natl. Acad. Sci. USA 111 7156

Cited By

[1]	Watts D J, Strogatz S H 1998 Nature 393 440
[2]	Barabási A L, Albert R 1999 Science 286 509
[3]	Lombardi A, Hörnquist M 2007 Phys. Rev. E 75 056110
[4]	Liu Y Y, Slotine J J, Barabrási A L 2011 Nature 473 167
[5]	Wang X F, Chen G R 2002 Physica A 310 521
[6]	Li X, Wang X F, Chen G R 2004 IEEE Trans. Circ. I 51 2074
[7]	Chen G R 2013 Acta Autom. Sin. 39 4
[8]	Chen G R 2014 Int. J. Control Autom. 12 221
[9]	Wang X F, Su H S 2005 Adv. Mech. 38 6 (in Chinese) [汪小帆, 苏厚胜 2005 力学进展 38 6]
[10]	Chen T P, Liu X W, Lu W L 2007 IEEE Trans. Circ. I 54 1317
[11]	Zhou J, Lu J A, L J H 2008 Automatica 44 996
[12]	Chen G R, Duan Z S 2008 Chaos 18 037102
[13]	Guo W L, Austin F, Chen S H, Sun W 2009 Phys. Lett. A 373 1565
[14]	Lin C T 1974 IEEE Trans. Automat. Control 19 201
[15]	Shields R W, Pearson J B 1976 IEEE Trans. Automat. Control. 21 203
[16]	Reinschke K J, Wiedemann G 1997 Linear Algebra Appl. 266 199
[17]	Sontag E D 1998 Mathematical Control Theory: Deterministic Finite Dimensional Systems (New York: Springer) p12
[18]	Lovász L, Plummer M D 1986 Matching Theory (North Holland: Elsevier Science Publishing Company) p113
[19]	Mulmuley K, Vazirani U V, Vazirani V V 1987 Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing p345
[20]	Umeyama S 1988 IEEE Trans. Pattern Anal. 10 695
[21]	Hopcroft J E, Karp R M 1973 Siam J. Comput. 2 225
[22]	Kalman R E 1963 J. Soc. Indus. Appl. Math. Ser. A 1 152
[23]	Poljak S 1990 IEEE Trans. Automat. Control 35 367
[24]	Yuan Z Z, Zhao C, Di Z R, Wang W X, Lai Y C 2013 Nat. Comm. 4 3447
[25]	Nepusz T, Vicsek T 2012 Nat. Phys. 8 568
[26]	Cowan N J, Chastain E J, Vilhena D A, Freudenberg J S, Bergstrom C T 2012 PloS One 7 e38398
[27]	Pósfai M, Liu Y Y, Slotine J J, Barabási A L 2013 Sci. Rep. 3 1065
[28]	Barrat A, Weigt M 2000 Eur. Phys. J. B 13 547
[29]	Leicht E A, Newman M E J 2008 Phys. Rev. Lett. 100 118703
[30]	Foster J G, Foster D V, Grassberger P, Paczuski M 2010 Proc. Natl. Acad. Sci. USA 107 10815
[31]	Menichetti G, Dall’Asta L, Bianconi G 2014 Phys. Rev. Lett. 113 078701
[32]	Hou L L, Small M, Lao S Y 2014 Phys. Lett. A 378 3426
[33]	Ruths J, Ruths D 2014 Science 343 1373
[34]	Onnela J P 2014 Science 21 1325
[35]	Wang B B, Gao L, Gao Y 2012 J. Stat. Mech. 2012 P04011
[36]	Liu Y Y, Slotine J J, Barabási A L 2012 PloS One 7 e44459
[37]	Jia T, Barabási A L 2013 Sci. Rep. 3 2354
[38]	Jia T, Liu Y Y, Csoka E, Posfai M, Slotine J J, Barabási A L 2013 Nat. Comm. 4 2002
[39]	Liu Y Y, Csoka E, Zhou H J, Posfai M 2012 Phys. Rev. Lett. 109 205703
[40]	Jia T, Posfai M 2014 Sci. Rep. 4 5379
[41]	Albert R, Jeong H, Barabási A L 2000 Nature 406 378
[42]	Buldyrev S V, Parshani R, Paul G, Stanley H E 2010 Nature 464 1025
[43]	Holme P, Kim B J, Yoon C N, Han S K 2002 Phys. Rev. E 65 056109
[44]	Callaway D S, Newman M E J, Strogatz S H, Watts D J 2000 Phys. Rev. Lett. 85 5468
[45]	Schwarte N, Cohen R, Ben-Avraham D, Barabási A L, Havlin S 2002 Phys. Rev. E 66 015104
[46]	Shargel B, Sayama H, Epstein I R, Bar-Yam Y 2003 Phys. Rev. Lett. 90 068701
[47]	Pu C L, Pei W J, Michaelson A 2012 Physica A 391 4420
[48]	Nie S, Wang X, Zhang H, Li Q, Wang B 2014 PLoS One 9 e89066
[49]	Wang B, Gao L, Gao Y, Deng Y 2013 EPL 101 58003
[50]	Xiao Y D, Lao S Y, Hou L L, Bai L 2014 Chin. Phys. B 23 118902
[51]	Xiao Y D, Lao S Y, Hou L L, Bai L 2013 Acta Phys. Sin. 62 180201(in Chinese) [肖延东, 老松杨, 侯绿林, 白亮 2013 物理学报 62 180201]
[52]	L T Y, Piao X F, Xie W Y, Huang S B 2012 Acta Phys. Sin. 61 170512(in Chinese) [吕天阳, 朴秀峰, 谢文艳, 黄少滨 2012 物理学报 61 170512]
[53]	Ruths J, Ruths D 2013 Complex Networks IV (New York: Springer) 476 185
[54]	Wang W X, Ni X, Lai Y C, Grebogi C 2012 Phys. Rev. E 85 026115
[55]	Hou L L, Lao S Y, Bu J, Bai L 2013 International Conference on Intelligent System Design and Engineering Applications 709
[56]	Hou L L, Lao S Y, Liu G, Bai L 2012 Chin. Phys. Lett. 29 108901
[57]	Xiao Y D, Lao SY, Hou L L, Bai L 2014 Phys. Rev. E 90 042804
[58]	Ding J, Lu Y Z, Chu J 2013 Physica A 392 6603
[59]	Yan G, Ren J, Lai Y C, Lai C H, Li B W 2012 Phys. Rev. Lett. 108 218703
[60]	Delpini D, Battiston S, Riccaboni M, Gabbi G, Pammolli F, Caldarelli G 2013 Sci. Rep. 3 1626
[61]	Wuchty S 2014 Proc. Natl. Acad. Sci. USA 111 7156

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Vol. 64, Issue 18 - 2015-09-20

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