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Problems and methods of network control

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Abstract

Control of network systems, or network control, is a rapidly developing field of modern automated control theory. Network control is characterized by a combination of the classical control theory toolbox (linear systems, nonlinear control, robust control and so on) and conceptually new mathematical ideas that come primarily from graph theory. Methods of network control let one solve analysis and synthesis problems for complex systems that arise in physics, biology, economics, sociology, and engineering sciences. In this survey, we present the main fields of application for modern theory of network control and formulate its key results obtained over the last decade.

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References

  1. Albert, R. and Barabasi, A.-L., Statistical Mechanics of Complex Networks, Rev. Mod. Phys., 2002, vol. 74, pp. 47–97.

    Article  MathSciNet  MATH  Google Scholar 

  2. Fax, J.A. and Murray, R.M., Information Flow and Cooperative Control of Vehicle Formations, IEEE Trans. Autom. Control, 2004, vol. 49, no. 9, pp. 1465–1476.

    Article  MathSciNet  Google Scholar 

  3. Olfati-Saber, R. and Murray, R.M., Consensus Problems in Networks of Agents with Switching Topology and Time-Delays, IEEE Trans. Autom. Control, 2004, vol. 49, no. 9, pp. 1520–1533.

    Article  MathSciNet  Google Scholar 

  4. Olfati-Saber, R., Fax, J.A., and Murray, R.M., Consensus and Cooperation in Networked Multi-Agent Systems, Proc. IEEE, 2007, vol. 95, no. 1, pp. 215–233.

    Article  Google Scholar 

  5. IEEE Control Syst. Mag., Special Section “Complex Networked Control Systems,” Aug. 2007.

  6. IEEE Trans. Automatic Control, “Special Issue on Networked Control Systems,” Sept., 2004.

  7. Proc. IEEE, Special Issue on Networked Control Systems Technology, January 2007.

  8. Physica D: Nonlinear Phenomena, Special Issue Evolving Dynam. Networks, Belykh, I., di Bernardo, M., Kurths, J., and Porfiri, M., Eds., 2014, vol. 267

  9. IFAC Workshops Distributed Estimat. Control Networked Syst., NecSys’09, 24–26 Sept., 2009, Venice, Italy; NecSys’10, 13–14 Sept., 2010, Grenoble, France; NecSys’11, 14–15 Sept., 2012, Santa Barbara, California; NecSys’13, 25–26 Sept., 2013, Koblenz, Germany; NecSys’15, 10–11 Sept., 2015, Philadelphia, USA.

  10. Tsypkin, Ya.Z., Adaptatsiya i obuchenie v avtomaticheskikh sistemakh (Adaptation and Learning in Automated Systems), Moscow: Nauka, 1968.

    Google Scholar 

  11. Andrievskii, B.R., Matveev, A.S., and Fradkov, A.S., Control and Estimation under Information Constraints: Toward a Unified Theory of Control, Computation and Communications, Autom. Remote Control, 2010, vol. 71, no. 4, pp. 572–633.

    Article  MathSciNet  MATH  Google Scholar 

  12. Hespanha, J.P., Naghshtabrizi, P., and Xu, Y., A Survey of Recent Results in Networked Control Systems, Proc. IEEE, 2007, vol. 95, no. 1, pp. 138–162.

    Article  Google Scholar 

  13. Matveev, A.S. and Savkin, A.V., Estimation and Control over Communication Networks, Boston: Birkhäuser, 2009.

    MATH  Google Scholar 

  14. Ren, W. and Cao, W., Distributed Coordination of Multi-Agent Networks, London: Springer-Verlag, 2011.

    Book  MATH  Google Scholar 

  15. Sarlette, A., Sepulchre, R., and Leonard, N., Autonomous Rigid Body Attitude Synchronization, Automatica, 2009, vol. 45, no. 2, pp. 572–577.

    Article  MathSciNet  MATH  Google Scholar 

  16. Egerstedt, M., Hu, X., and Stotsky, A., Control of Mobile Platforms Using a Virtual Vehicle Approach, IEEE Trans. Autom. Control, 2001, vol. 46, no. 11, pp. 1777–1782.

    Article  MathSciNet  MATH  Google Scholar 

  17. Olfati-Saber, R., Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory, IEEE Trans. Autom. Control, 2006, vol. 51, no. 3, pp. 401–420.

    Article  MathSciNet  Google Scholar 

  18. Tanner, H.G., Jadbabaie, A., and Pappas, G.J., Flocking in Fixed and Switching Networks, IEEE Trans. Autom. Control, 2007, vol. 52, no. 5, pp. 863–868.

    Article  MathSciNet  Google Scholar 

  19. Li, W., Stability Analysis of Swarms with General Topology, IEEE Trans. Syst., Man, Cybern., B, 2008, vol. 38, no. 4, pp. 1084–1097.

    Article  Google Scholar 

  20. Lin, J., Morse, A.S., and Anderson, B.D.O., The Multi-Agent Rendezvous Problem (in 2 parts), SIAM J. Control Optim., 2007, vol. 46, no. 6, pp. 2096–2147.

    Article  MathSciNet  MATH  Google Scholar 

  21. Cortes, J., Martinez, S., and Bullo, F., Robust Rendezvous for Mobile Autonomous Agents via Proximity Graphs in Arbitrary Dimensions, IEEE Trans. Autom. Control, 2006, vol. 51, no. 8, pp. 1289–1298.

    Article  MathSciNet  Google Scholar 

  22. Martinez, S., Bullo, F., Cortes, J., and Frazzoli, E., On Synchronous Robotic Networks (in 2 parts), IEEE Trans. Autom. Control, 2007, vol. 52, no. 12, pp. 2199–2226.

    Article  MathSciNet  Google Scholar 

  23. Ren, W., Formation Keeping and Attitude Alignment for Multiple Spacecraft Through Local Interactions, J. Guid. Control Dynam., 2007, vol. 30, no. 2, pp. 633–638.

    Article  Google Scholar 

  24. Li, Z., Duan, Z., Chen, G., and Huang, L., Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint, IEEE Trans. Circuits Syst., I, 2010, vol. 57, no. 1, pp. 213–224.

    Article  MathSciNet  Google Scholar 

  25. Fradkov, A.L., Kiberneticheskaya fizika (Cybernetic Physics), St. Petersburg: Nauka, 2003.

    Google Scholar 

  26. Blekhman, I.I. and Fradkov, A.L., On General Definitions of Synchronization, in Selected Topics in Vibrational Mechanics, Singapore: World Scientific, 2004, pp. 179–188.

    Chapter  Google Scholar 

  27. Ren, W. and Beard, R., Distributed Consensus in Multi-Vehicle Cooperative Control: Theory and Applications, London: Springer-Verlag, 2008.

    Book  MATH  Google Scholar 

  28. Agaev, R.P. and Chebotarev, P.Yu., Convergence and Stability in Characteristic Coordination Problems, Upravlen. Bol’shimi Sist., 2010, no. 30.1, pp. 470–505.

    Google Scholar 

  29. Dzhunusov, I.A. and Fradkov, A.L., Synchronization in Networks of Linear Agents with Output Feedbacks, Autom. Remote Control, 2011, vol. 72, no. 8, pp. 1615–1626.

    Article  MathSciNet  MATH  Google Scholar 

  30. Fradkov, A.L., Junussov, I., and Ortega, R., Decentralized Adaptive Synchronization in Nonlinear Dynamical Networks with Nonidentical Nodes, IEEE Multiconf. Syst. Control (MSC 2009), St. Petersburg, Russia, 2009, pp. 531–536.

    Google Scholar 

  31. Fradkov, A.L. and Junussov, I., Output Feedback Synchronization for Networks of Linear Agents, Eur. Nonlinear Dynam. Conf. (ENOC 2011), Rome, Italy, 2011.

    Google Scholar 

  32. Fradkov, A.L. and Junussov, I.A., Synchronization of Networks of Linear Systems by Static Output Feedback, IEEE Conf. Decision Control (CDC 2011), Orlando, USA, 2011, pp. 8188–8192.

    Google Scholar 

  33. Fradkov, A.L., Grigoriev, G.K., and Selivanov, A.A., Decentralized Adaptive Controller for Synchronization of Dynamical Networks with Delays and Bounded Disturbances, IEEE Conf. Decision Control (CDC 2011), Orlando, USA, 2011, pp. 1110–1115.

    Google Scholar 

  34. Selivanov, A.A., Fradkov, A.L., and Fridman, E., Adaptive Synchronization of Networks with Delays under Incomplete Control and Incomplete Measurements, 18 IFAC World Congr. Autom. Control, Milan, Italy, 2011, pp. 1249–1254.

    Google Scholar 

  35. Moyne, J.R. and Tilbury, D.M., The Emergence of Industrial Control Networks for Manufacturing Control, Diagnostics, and Safety Data, Proc. IEEE, 2007, vol. 95, no. 1, pp. 29–47.

    Article  Google Scholar 

  36. Coe, N.M., Dicken, P., and Hess, M., Global Production Networks: Realizing the Potential, J. Econom. Geograph., 2008, vol. 8, no. 3, pp. 271–295.

    Article  Google Scholar 

  37. Jiao, J.X., You, X., and Kumar, A., An Agent-Based Framework for Collaborative Negotiation in the Global Manufacturing Supply Chain Network, Robot. Comput. Integrat. Manufactur., 2006, vol. 22, no. 3, pp. 239–255.

    Article  Google Scholar 

  38. Garlaschelli, D. and Loffredo, M., Structure and Evolution of the World Trade Network, Phys. A, 2006, vol. 355, no. 1, pp. 138–144.

    Article  MathSciNet  Google Scholar 

  39. Garlaschelli, D. and Loffredo, M., Effects of Network Topology on Wealth Distributions, J. Phys. A, 2004, vol. 41, no. 22, pp. 224018.

    Article  MathSciNet  MATH  Google Scholar 

  40. Easley, D. and Kleinberg, J., Networks, Crowds and Markets. Reasoning about a Highly Connected World, Cambridge: Cambridge Univ. Press, 2010.

    Book  MATH  Google Scholar 

  41. Mesbahi, M. and Egerstedt, M., Graph Theoretic Methods in Multiagent Networks, Princeton: Princeton Univ. Press, 2010.

    Book  MATH  Google Scholar 

  42. Kalyaev, I.A., Organization Principles for Decentralized Control Systems for Collectives of Microrobots, Mekhatronika, 2000, no.6.

  43. Kalyaev, I.A., Gaiduk, A.R., and Kapustyan, S.G., Modeli i algoritmy kollektivnogo upravleniya v gruppakh robotov (Collective Control Models and Algorithms in Groups of Robots), Moscow: Fizmatlit, 2009.

    Google Scholar 

  44. Bullo, F., Cortes, J., and Martinez, S., Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms, Princeton: Princeton Univ. Press, 2009.

    Book  MATH  Google Scholar 

  45. Lewis, F.L., Zhang, H., Hengster-Movric, K., and Das, A., Cooperative Control of Multi-Agent Systems: Optimal Design and Adaptive Control, Berlin: Springer-Verlag, 2014.

    Book  MATH  Google Scholar 

  46. Abdessameud, A. and Tayebi, A., Motion Coordination for VTOL Unmanned Aerial Vehicles, Berlin: Springer-Verlag, 2013.

    Book  MATH  Google Scholar 

  47. D’Andrea, R., Acrobatic Flight (Plenary Lecture), IEEE Conf. Decision Control (CDC 2013), Florence, Italy, 2013.

    Google Scholar 

  48. D’Andrea, R., The Astounding Athletic Power of Quadcopters, https://www.ted.com/talks/raffaello d andrea the astounding athletic power of quadcopters.

  49. Augugliaro, F., Schoellig, A., and D’Andrea, R., Dance of the Flying Machines, IEEE Robot. Autom. Mag., 2013, vol. 20, no. 4, pp. 96–104.

    Article  Google Scholar 

  50. Hoy, M., Matveev, A., and Savkin, A.V., Algorithms for Collision-Free Navigation of Mobile Robots in Complex Cluttered Environments: A Survey, Robotica, 2015, vol. 33, no. 3, pp. 463–497.

    Article  Google Scholar 

  51. Hill, D.J. and Chen, G., Power Systems as Dynamic Networks, IEEE Int. Symp. Circuits Syst., Kos, Greece, 2006, pp. 722–725.

    Google Scholar 

  52. Doerfler, F., Chertkov, M., and Bullo, F., Synchronization in Complex Oscillator Networks and Smart Grids, PNAS, 2013, vol. 110, no. 6, pp. 2005–2010.

    Article  MathSciNet  MATH  Google Scholar 

  53. Butler, F., A Call to Order a Regulatory Perspective on the Smart Grid, IEEE Power Energy Mag., 2009, no. 2, pp. 16–93.

    Article  Google Scholar 

  54. Farhangi, H., The Path of the Smart Grid, IEEE Power Energy Mag., 2010, no. 1, pp. 18–28.

    Article  Google Scholar 

  55. Jackson, J., Improving Energy and Smart Grid Program Analysis with Agent-Based End-Use Forecasting Models, Energy Policy, 2010, vol. 38, pp. 3771–3780.

    Article  Google Scholar 

  56. Liserre, M., Sauter, T., and Hung, Y.J., Future Energy Systems: Integrating Renewable Energy Sources into the Smart Power Grid Through Industrial Electronics, IEEE Ind. Electron. Mag., 2010, vol. 4, no. 1, pp. 18–37.

    Article  Google Scholar 

  57. Dorofeev, V.V. and Makarov, A.A., Smart Grid as a New Quality of Russian Electrical Energy Networks, Energoekspert, 2009, no. 4, pp. 28–34.

    Google Scholar 

  58. Pchelkina, I.V. and Fradkov, A.L., Modeling the Control Process over Synchronization of a Multi-Machine Power System, Informat. Sist. Upravlen., 2012, no. 4, pp. 18–26.

    Google Scholar 

  59. Fradkov, A.L. and Furtat, I.B., Robust Control for a Network of Electric Power Generators, Autom. Remote Control, 2013, vol. 74, no. 11, pp. 1851–1862.

    Article  MathSciNet  MATH  Google Scholar 

  60. Furtat, I.B., Control over an Electric Power Network with Regard to its Topology, Mekhatronika, Avtomatiz., Upravlen., 2013, no. 4, pp. 33–38.

    Google Scholar 

  61. Furtat, I.B. and Fradkov, A.L., Robust Control of Multi-Machine Power Systems with Compensation of Disturbances, Int. J. Elect. Power Energy Syst., 2015, vol. 73, pp. 584–590.

    Article  Google Scholar 

  62. Kleinrock, L., Communication Nets: Stochastic Message Flow and Delay, New York: McGraw-Hill, 1964. Translated under the title Kommunikatsionnye seti: stokhasticheskie potoki i zaderzhki soobschenii, Moscow: Nauka, 1970.

    MATH  Google Scholar 

  63. Baran, P., On Distributed Communication Networks, IEEE Trans. Commun. Syst., 1964, vol. 12, no. 1, pp. 1–9.

    Article  Google Scholar 

  64. Lindsey, W.C., Ghazvinian, F., Hagmann, W.G., et al., Network Synchronization, Proc. IEEE, 1985, vol. 73, no. 10, pp. 1445–1467.

    Article  Google Scholar 

  65. Schenato, L. and Fiorentin, F., Average TimeSynch: A Consensus-Based Protocol for Clock Synchronization in Wireless Sensor Networks, Automatica, 2011, vol. 47, no. 9, pp. 1878–1886.

    Article  MathSciNet  MATH  Google Scholar 

  66. Carli, R. and Zampieri, S., Network Clock Synchronization Based on the Second-Order Linear Consensus Algorithm, IEEE Trans. Autom. Control, 2014, vol. 59, no. 2, pp. 409–422.

    Article  MathSciNet  Google Scholar 

  67. Shivaratri, N.G., Krueger, P., and Singhal, M., Load Distributing for Locally Distributed Systems, Computer, 1992, vol. 25 No. 12, pp. 33–44.

    Article  Google Scholar 

  68. Amelina, N.O. and Fradkov, A.L., Approximate Consensus in the Dynamic Stochastic Network with Incomplete Information and Measurement Delays, Autom. Remote Control, 2012, vol. 73, no. 11, pp. 1765–1783.

    Article  MathSciNet  MATH  Google Scholar 

  69. Amelina, N., Fradkov, A., Jiang, Yu., and Vergados, D.J., Approximate Consensus in Stochastic Networks with Application to Load Balancing, IEEE Trans. Inform. Theory, 2015, vol. 61, no. 4, pp. 1739–1752.

    Article  MathSciNet  Google Scholar 

  70. Williams, R.J. and Martinez, N.D., Simple Rules Yield Complex Food Webs, Nature, 2000, vol. 404, no. 9, pp. 180–183.

    Article  Google Scholar 

  71. Pchelkina, I.V. and Fradkov, A.L., Control of Oscillatory Behavior of Multispecies Populations, Ecologic. Model., 2012, vol. 227, pp. 1–6.

    Article  Google Scholar 

  72. Zeeman, E.C., Dynamics of the Evolution of Animal Conflicts, J. Theor. Biol., 1981, vol. 89, pp. 249–270.

    Article  MathSciNet  Google Scholar 

  73. Weibull, J.W., Evolutionary Game Theory, Cambridge: MIT Press, 1995.

    MATH  Google Scholar 

  74. Mirollo, R.E. and Strogatz, S.H., Synchronization of Pulse-Coupled Biological Oscillators, SIAM J. Appl. Math., 1990, vol. 50, no. 6, pp. 1645–1662.

    Article  MathSciNet  MATH  Google Scholar 

  75. Vasalou, C. and Henson, M.A., A Multicellular Model for Differential Regulation of Circadian Signals in the Shell and Core Regions of the SCN, J. Theor. Biol., 2011, vol. 288, pp. 44–56.

    Article  Google Scholar 

  76. Ovod, I.V., Osadchii, A.E., Pupyshev, A.A., and Fradkov, A.L., Forming a Neurofeedback Connection based on an Adaptive Model of Brain Acticity, Neirokomp’yutery, 2012, no. 2, pp. 36–41.

    Google Scholar 

  77. Hein, S.M., Schulze, F., Carmele, A., and Knorr, A., Entanglement Control in Quantum Networks by Quantum-Coherent Time-Delayed Feedback, Phys. Rev. A, 2015, no. 91, p. 052321.

    Article  Google Scholar 

  78. Besekerskii, V.A. and Popov, E.P., Teoriya sistem avtomaticheskogo regulirovaniya (Theory of Automated Control Systems), Moscow: Nauka, 1966.

    MATH  Google Scholar 

  79. Wonham, W.M., Linear Multivariable Control: A Geometric Approach, New York: Springer-Verlag, 1979. Translated under the title Lineinye mnogomernye sistemy upravleniya. Geometricheskii podkhod, Moscow: Nauka, 1980.

    Book  MATH  Google Scholar 

  80. Ray, W.H., Advanced Process Control, New York: McGraw Hill, 1980. Translated under the title Metody upravleniya tekhnologicheskimi protsessami, Moscow: Mir, 1983.

    Google Scholar 

  81. Sobolev, O.S., Metody issledovaniya lineinykh mnogosvyaznykh sistem (Methods for Studying Linear Multiconnected Systems), Moscow: Energiya, 1985.

    Google Scholar 

  82. Meerov, M.V., Issledovanie i optimizatsiya mnogosvyaznykh sistem upravleniya (Studies and Optimization of Multivariable Control Systems), Moscow: Nauka, 1986.

    MATH  Google Scholar 

  83. Pogromsky, A., Santoboni, G., and Nijmeijer, H., Partial Synchronization: From Symmetry Towards Stability, Phys. D, 2002, vol. 172, pp. 65–87.

    Article  MathSciNet  MATH  Google Scholar 

  84. Blekhman, I.I., Sinkhronizatsiya dinamicheskikh sistem (Synchronization of Dynamical Systems), Moscow: Nauka, 1971.

    MATH  Google Scholar 

  85. Gurtovnik, A.S. and Neimark, Yu.I., On Synchronization in Dynamical Systems, Prikl. Mat. Mekh., 1974, vol. 38, no. 5, pp. 799–809.

    MathSciNet  Google Scholar 

  86. Blekhman, I.I., Vibratsionnaya mekhanika (Vibrational Mechanics), Moscow: Nauka, 1994.

    Google Scholar 

  87. Lindsey, W.C., Synchronization Systems in Communication and Control, New York: Pearson Education, 1972.

    Google Scholar 

  88. Leonov, G.A. and Smirnova, V.B., Matematicheskie problemy teorii fazovoi sinkhronizatsii (Mathematical Problems of Phase Synchronization Theory), St. Petersburg: Nauka, 2000.

    Google Scholar 

  89. Afraimovich, V.S., Verichev, N.N., and Rabinovich, M.I., Stochastic Synchronization of Oscillations in Dissipative Systems, Izv. Vyssh. Uchebn. Zaved., Radiophys., 1986, vol. 29, no. 9, pp. 1050–1060.

    MathSciNet  Google Scholar 

  90. Pecora, L.M. and Carroll, T.L., Synchronization in Chaotic Systems, Phys. Rev. Lett., 1990, vol. 64, pp. 821–823.

    Article  MathSciNet  MATH  Google Scholar 

  91. Rulkov, N.F., Sushchik, M., Tsimring, L.S., and Abarbanel, H.D.I., Generalized Synchronization of Chaos, Phys. Rev. E, 1995, vol. 51, pp. 980.

    Article  Google Scholar 

  92. Rosenblum, M.G, Pikovsky, A.S., and Kurths, J., Phase Synchronization of Chaotic Oscillators, Phys. Rev. Lett., 1996, vol. 76, pp. 1804–1807.

    Article  MATH  Google Scholar 

  93. Blekhman, I.I., Fradkov, A.L., Nijmeijer, H., and Pogromsky, A.Yu., On Self-Synchronization and Controlled Synchronization, Syst. Control Lett., 1997, vol. 31, pp. 299–305.

    Article  MathSciNet  MATH  Google Scholar 

  94. Upravlenie mekhatronnymi vibratsionnymi ustanovkami (Control for Mechatronic Vibration Equipment), Blekhman, I.I. and Fradkov, A.L., Eds., St. Petersburg: Nauka, 2001.

  95. Blekhman, I.I., Fradkov, A.L., Tomchina, O.P., and Bogdanov, D.E., Self-Synchronization and Controlled Synchronization: General Definition and Example Design, Math. Comput. Simulat., 2002, vol. 58, nos. 4–6, pp. 367–384.

    Article  MathSciNet  MATH  Google Scholar 

  96. Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.L., Nelineinoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemami (Nonlinear and Adaptive Control over Complex Dynamical Systems), St. Petersburg: Nauka, 2000.

    Google Scholar 

  97. French, J., A Formal Theory of Social Power, Psych. Rev., 1956, vol. 63, pp. 181–194.

    Article  MathSciNet  Google Scholar 

  98. Harary, F., A Criterion for Unanimily in French’s Theory of Social Power, in Studies in Social Power, Dorwin Cartwright, Ed., Ann Arbor: Univ. of Michigan, 1959, pp. 168–182.

    Google Scholar 

  99. Eisenberg, E. and Gale, D., Consensus of Subjective Probabilities: The Pari-Mutuel Method, Ann. Math. Statist., 1959, vol. 30, pp. 165–168.

    Article  MathSciNet  MATH  Google Scholar 

  100. DeGroot, M.H., Reaching a Consensus, J. Am. Statist. Assoc., 1974, vol. 69, no. 345, pp. 118–121.

    Article  MATH  Google Scholar 

  101. Reynolds, S., Flocks, Herds, and Schools: A Distributed Behavioral Model, Comput. Graphics, 1987, vol. 21, no. 4, pp. 25–34.

    Article  Google Scholar 

  102. Jadbabaie, A., Lin, J., and Morse, A.S., Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules, IEEE Trans. Autom. Control, 2003, vol. 48, no. 6, pp. 988–1001.

    Article  MathSciNet  Google Scholar 

  103. Wieland, P., Sepulchre, R., and Allgower, F., An Internal Model Principle is Necessary and Sufficient for Linear Output Synchronization, Automatica, 2011, vol. 47, pp. 1068–1074.

    Article  MathSciNet  MATH  Google Scholar 

  104. Isidori, A., Marconi, L., and Casadei, G., Robust Output Synchronization of a Network of Heterogeneous Nonlinear Agents via Nonlinear Regulation Theory, IEEE Trans. Autom. Control, 2014, vol. 59, no. 10, pp. 2680–2691.

    Article  MathSciNet  Google Scholar 

  105. Polyak, B.T. and Tsypkin, Ya.Z., Stability and Robust Stability of Uniform Systems, Autom. Remote Control, 1996, vol. 57, no. 11, pp. 1606–1617.

    MathSciNet  MATH  Google Scholar 

  106. Hara, S., Tanaka, H., and Iwasaki, T., Stability Analysis of Systems with Generalized Frequency Variables, IEEE Trans. Autom. Control, 2014, vol. 59, no. 2, pp. 313–326.

    Article  MathSciNet  Google Scholar 

  107. Pecora, L.M. and Carroll, T.L., Master Stability Functions for Synchronized Coupled Systems, Phys. Rev. Lett., 1998, vol. 80, pp. 2109–2112.

    Article  Google Scholar 

  108. Tsitsiklis, J.N., Bertsekas, D.P., and Athans, M., Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms, IEEE Trans. Autom. Control, 1986, vol. 31, no. 9, pp. 803–812.

    Article  MathSciNet  MATH  Google Scholar 

  109. Hatanaka, T., Chopra, N., Fujita, M., and Spong, M.W., Passivity-Based Control and Estimation in Networked Robotics, New York: Springer-Verlag, 2015.

    Book  MATH  Google Scholar 

  110. Arcak, M., Passivity as a Design Tool for Group Coordination, IEEE Trans. Autom. Control, 2007, vol. 52, no. 8, pp. 1380–1390.

    Article  MathSciNet  Google Scholar 

  111. Proskurnikov, A., Zhang, F., Cao, M., and Scherpen, J.M.A., A General Criterion for Synchronization of Incrementally Dissipative Nonlinearly Coupled Agents, Proc. Eur. Control Conf. (ECC), 2015, pp. 581–586.

    Google Scholar 

  112. Proskurnikov, A.V., Average Consensus in Networks with Nonlinearly Delayed Couplings and Switching Topology, Automatica, 2013, vol. 49, no. 9, pp. 2928–2932.

    Article  MathSciNet  Google Scholar 

  113. Proskurnikov, A.V., Delay Robustness of Nonlinear Consensus Protocols: Analytic Criteria, in Recent Results on Time-Delay Systems, Witrant, E., et al., Eds., New York: Springer, 2016, pp. 125–146.

    Chapter  Google Scholar 

  114. Proskurnikov, A.V. and Shakhova, N.D., Consensus Robustness Against Inner Delays, Electr. Notes Discr. Math., 2016, vol. 51, pp. 7–14.

    Article  MathSciNet  Google Scholar 

  115. Ren, W. and Beard, R.W., Consensus Seeking in Multiagent Systems under Dynamically Changing Interaction Topologies, IEEE Trans. Autom. Control, 2005, vol. 50, no. 5, pp. 655–661.

    Article  MathSciNet  Google Scholar 

  116. Papachristodoulou, A., Jadbabaie, A., and Münz, U., Effects of Delay in Multi-Agent Consensus and Oscillator Synchronization, IEEE Trans. Autom. Control, 2010, vol. 55, no. 6, pp. 1471–1477.

    Article  MathSciNet  Google Scholar 

  117. Matveev, A.S., Novinitsyn, I., and Proskurnikov, A.V., Stability of Continuous-Time Consensus Algorithms for Switching Networks with Bidirectional Interaction, Eur. Control Conf. (ECC), 2013, pp. 1872–1877.

    Google Scholar 

  118. Hendricx, J. and Tsitsiklis, J.N., Convergence of Type-Symmetric and Cut-Balanced Consensus Seeking Systems, IEEE Trans. Autom. Control, 2013, vol. 58, no. 1, pp. 214–218.

    Article  MathSciNet  Google Scholar 

  119. Moreau, L., Stability of Multiagent Systems with Time-Dependent Communication Links, IEEE Trans. Autom. Control, 2005, vol. 50, no. 2, pp. 169–182.

    Article  MathSciNet  Google Scholar 

  120. Agaev, R.P. and Chebotarev, P.Yu., The Matrix of Maximal Outgoing Forests of a Digraph and Its Applications, Autom. Remote Control, 2000, vol. 61, no. 9, pp. 1424–1450.

    MathSciNet  MATH  Google Scholar 

  121. Agaev, R. and Chebotarev, P., On the Spectra of Nonsymmetric Laplacian Matrices, Linear Algebra Appl., 2005, vol. 399, pp. 157–168.

    Article  MathSciNet  MATH  Google Scholar 

  122. Chebotarev, P. and Agaev, R., The Forest Consensus Theorem, IEEE Trans. Autom. Control, 2014, vol. 59, no. 9, pp. 2475–2479.

    Article  MathSciNet  Google Scholar 

  123. Yu, W., Chen, G., and Cao, M., Some Necessary and Sufficient Conditions for Second-Order Consensus in Multi-Agent Dynamical Systems, Automatica, 2010, vol. 46, no. 6, pp. 1089–1095.

    Article  MathSciNet  MATH  Google Scholar 

  124. Yu, W., Zheng, W.X., Chen, G., Ren, W., and Cao, J., Second-Order Consensus in Multi-Agent Dynamical Systems with Sampled Position Data, Automatica, 2011, vol. 47, no. 6, pp. 1496–1503.

    Article  MathSciNet  MATH  Google Scholar 

  125. Proskurnikov, A., Consensus in Switching Networks with Sectorial Nonlinear Couplings: Absolute Stability Approach, Automatica, 2013, vol. 49, no. 2, pp. 488–495.

    Article  MathSciNet  MATH  Google Scholar 

  126. Proskurnikov, A., Nonlinear Consensus Algorithms with Uncertain Couplings, Asian J. Control, 2014, vol. 16, no. 5, pp. 1277–1288.

    Article  MathSciNet  MATH  Google Scholar 

  127. Proskurnikov, A.V., Frequency-Domain Criteria for Consensus in Multiagent Systems with Nonlinear Sector-Shaped Couplings, Autom. Remote Control, 2014, vol. 75, no. 11, pp. 1982–1995.

    Article  MathSciNet  MATH  Google Scholar 

  128. Proskurnikov, A.V. and Matveev, A., Popov-Type Criterion for Consensus in Nonlinearly Coupled Networks, IEEE Trans. Cybern., 2015, vol. 45, no. 8, pp. 1537–1548.

    Article  Google Scholar 

  129. Proskurnikov, A.V., Consensus in Nonlinear Stationary Networks with Identical Agents, Autom. Remote Control, 2015, vol. 76, no. 9, pp. 1551–1565.

    Article  MathSciNet  MATH  Google Scholar 

  130. Grigoriev, R.O., Cross, M.C., and Schuster, H.G., Pinning Control of Spatiotemporal Chaos, Phys. Rev. Lett., 1997, vol. 79, no. 15, pp. 2795–2798.

    Article  Google Scholar 

  131. Wang, X.F. and Chen, G., Pinning Control of Scale Free Dynamical Networks, Phys. A, 2002, vol. 310, pp. 521–531.

    Article  MathSciNet  MATH  Google Scholar 

  132. Li, X., Wang, X.F., and Chen, G., Pinning a Complex Dynamical Network to Its Equilibrium, IEEE Trans. Circuit Syst., I, 2004, vol. 51, no. 10, pp. 2074–2087.

    MathSciNet  Google Scholar 

  133. Cho, A., Scientific Link-Up Yields “Control Panel” for Networks, Sci., 2011, vol. 332, p. 777.

    Article  Google Scholar 

  134. Couzin, I.D., Krause, J., Franks, N.R., and Levin, S.A., Effective Leadership and Decision Making in Animal Groups on the Move, Nature, 2005, vol. 433, p. 513.

    Article  Google Scholar 

  135. Yu, W., Chen, G., and Lü, J., On Pinning Synchronization of Complex Dynamical Networks, Automatica, 2009, vol. 45, no. 2, pp. 429–435.

    Article  MathSciNet  MATH  Google Scholar 

  136. Yu, W., Chen, G., Lü, J., and Kurths, J., Synchronization via Pinning Control on General Complex Networks, SIAM J. Control Optim., 2013, vol. 51, no. 2, pp. 1395–1416.

    Article  MathSciNet  MATH  Google Scholar 

  137. Cao, Y., Yu, W., Ren, W., and Chen, G., An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination, IEEE Trans. Industr. Inform., 2013, vol. 9, no. 1, pp. 427–438.

    Article  Google Scholar 

  138. Chen, G., Pinning Control and Synchronization on Complex Dynamical Networks, Int. J. Control Autom. Syst., 2014, vol. 12, no. 2, pp. 221–230.

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

    A. V. Proskurnikov & A. L. Fradkov

  2. St. Petersburg State University, St. Petesrburg, Russia

    A. V. Proskurnikov & A. L. Fradkov

  3. ITMO University, St. Petersburg, Russia

    A. V. Proskurnikov & A. L. Fradkov

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  1. A. V. Proskurnikov
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  2. A. L. Fradkov
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Original Russian Text © A.V. Proskurnikov, A.L. Fradkov, 2016, published in Avtomatika i Telemekhanika, 2016, No. 10, pp. 3–39.

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Proskurnikov, A.V., Fradkov, A.L. Problems and methods of network control. Autom Remote Control 77, 1711–1740 (2016). https://doi.org/10.1134/S0005117916100015

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