Pinning control and controllability of complex dynamical networks

In this article, the notion of pinning control for directed networks of dynamical systems is introduced, where the nodes could be either single-input single-output (SISO) or multi-input multi-output (MIMO) dynamical systems, and could be non-identical and nonlinear in general but will be specified to be identical linear time-invariant (LTI) systems here in the study of network controllability. Both state and structural controllability problems will be discussed, illustrating how the network topology, node-system dynamics, external control inputs and inner dynamical interactions altogether affect the controllability of a general complex network of LTI systems, with necessary and sufficient conditions presented for both SISO and MIMO settings. To that end, the controllability of a special temporally switching directed network of linear time-varying (LTV) node systems will be addressed, leaving some more general networks and challenging issues to the end for research outlook.

[1]  H.G. Tanner,et al.  On the controllability of nearest neighbor interconnections , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[2]  Jacques L. Willems,et al.  Structural controllability and observability , 1986 .

[3]  Yu Wang,et al.  Controllability and observability analysis for vertex domination centrality in directed networks , 2014, Scientific reports.

[4]  Lin Gao,et al.  Control range: a controllability-based index for node significance in directed networks , 2012 .

[5]  Tamás Vicsek,et al.  Controlling edge dynamics in complex networks , 2011, Nature Physics.

[6]  Guanrong Chen,et al.  Pinning synchronization of networked multi-agent systems: spectral analysis , 2015 .

[7]  Hai Lin,et al.  Structural controllability of switched linear systems , 2011, Autom..

[8]  John Lygeros,et al.  On Submodularity and Controllability in Complex Dynamical Networks , 2014, IEEE Transactions on Control of Network Systems.

[9]  Bidyadhar Subudhi,et al.  Cooperative formation control of autonomous underwater vehicles: An overview , 2016, Int. J. Autom. Comput..

[10]  A. Lombardi,et al.  Controllability analysis of networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Albert-László Barabási,et al.  Target control of complex networks , 2014, Nature Communications.

[12]  Supratim Ghosh,et al.  Structural control of single-input rank one bilinear systems , 2016, Autom..

[13]  Guanrong Chen,et al.  Linear systems and optimal control , 1989, Springer series in information sciences.

[14]  Airlie Chapman.  Strong Structural Controllability of Networked Dynamics , 2015 .

[15]  Guangming Xie,et al.  Controllability of a Leader–Follower Dynamic Network With Switching Topology , 2008, IEEE Transactions on Automatic Control.

[16]  Gunther Reissig,et al.  Strong Structural Controllability and Observability of Linear Time-Varying Systems , 2013, IEEE Transactions on Automatic Control.

[17]  Jari Saramäki,et al.  Temporal Networks , 2011, Encyclopedia of Social Network Analysis and Mining.

[18]  Guanrong Chen,et al.  Pinning control and synchronization on complex dynamical networks , 2014, International Journal of Control, Automation and Systems.

[19]  Albert-László Barabási,et al.  Observability of complex systems , 2013, Proceedings of the National Academy of Sciences.

[20]  Xiang Li,et al.  Structural Controllability and Controlling Centrality of Temporal Networks , 2014, PloS one.

[21]  Guanrong Chen,et al.  Pinning controllability of asymmetrical weighted scale-free networks , 2008 .

[22]  Christian Commault,et al.  Generic properties and control of linear structured systems: a survey , 2003, Autom..

[23]  Ginestra Bianconi,et al.  Network controllability is determined by the density of low in-degree and out-degree nodes. , 2014, Physical review letters.

[24]  H. Mayeda,et al.  Strong Structural Controllability , 1979 .

[25]  Ching-tai Lin.  Structural controllability , 1974 .

[26]  Z. Duan,et al.  Network synchronizability analysis: a graph-theoretic approach. , 2008, Chaos.

[27]  Xiang Li,et al.  Structural Controllability of Temporally Switching Networks , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[28]  Ferdinand Svaricek,et al.  Strong structural controllability of linear systems revisited , 2011, IEEE Conference on Decision and Control and European Control Conference.

[29]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[30]  Tao Jia,et al.  Control Capacity and A Random Sampling Method in Exploring Controllability of Complex Networks , 2013, Scientific Reports.

[31]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[32]  F. Garofalo,et al.  Controllability of complex networks via pinning. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  I. Couzin,et al.  Effective leadership and decision-making in animal groups on the move , 2005, Nature.

[34]  J. Slotine,et al.  Spectrum of controlling and observing complex networks , 2015, Nature Physics.

[35]  Guanrong Chen,et al.  Pinning control of scale-free dynamical networks , 2002 .

[36]  B. Bollobás.  The evolution of random graphs , 1984 .

[37]  Endre Csóka,et al.  Emergence of bimodality in controlling complex networks , 2013, Nature Communications.

[38]  J. Pearson,et al.  Structural controllability of multiinput linear systems , 1976 .

[39]  Xiang Li,et al.  Pinning a complex dynamical network to its equilibrium , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..

[40]  Y. Lai,et al.  Optimizing controllability of complex networks by minimum structural perturbations. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  Luis Mateus Rocha,et al.  Control of complex networks requires both structure and dynamics , 2015, Scientific Reports.

[42]  Maurizio Porfiri,et al.  Criteria for global pinning-controllability of complex networks , 2008, Autom..

[43]  A. Cho.  Physics. Scientific link-up yields 'control panel' for networks. , 2011, Science.

[44]  Wen-Xu Wang,et al.  Exact controllability of complex networks , 2013, Nature Communications.

[45]  Xiang Li,et al.  Towards Structural Controllability of Temporal Complex Networks , 2016 .

[46]  Ching-tai Lin.  System structure and minimal structural controllability , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[47]  Jie Ren,et al.  Controlling complex networks: How much energy is needed? , 2012, Physical review letters.

[48]  Guanrong Chen,et al.  Controllability of networked higher-dimensional systems with one-dimensional communication , 2017, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[49]  Jonathan J. H. Zhu,et al.  Controllability of Weighted and Directed Networks with Nonidentical Node Dynamics , 2013 .

[50]  Xiao Fan Wang,et al.  Pinning control of complex networked systems: A decade after and beyond , 2014, Annu. Rev. Control..

[51]  Márton Pósfai,et al.  Structural controllability of temporal networks , 2014 .

[52]  Lin Wang,et al.  Controllability of networked MIMO systems , 2015, Autom..

[53]  T. Carroll,et al.  MASTER STABILITY FUNCTIONS FOR SYNCHRONIZED COUPLED SYSTEMS , 1999 .

[54]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[55]  Huijun Gao,et al.  Evolutionary Pinning Control and Its Application in UAV Coordination , 2012, IEEE Transactions on Industrial Informatics.

[56]  Fangfei Li,et al.  Pinning Control Design for the Stabilization of Boolean Networks , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[57]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[58]  Hai Lin,et al.  A graph-theoretic characterization of structural controllability for multi-agent system with switching topology , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[59]  Albert-László Barabási,et al.  Control Principles of Complex Networks , 2015, ArXiv.

[60]  Albert-László Barabási,et al.  Controllability of complex networks , 2011, Nature.

[61]  Y.-Y. Liu,et al.  The fundamental advantages of temporal networks , 2016, Science.

[62]  L. Silverman,et al.  Controllability and Observability in Time-Variable Linear Systems , 1967 .

[63]  Tong Zhou,et al.  On the controllability and observability of networked dynamic systems , 2014, Autom..