Skip to main content
SpringerLink
Log in

Consensus in Asynchronous Multiagent Systems. I. Asynchronous Consensus Models

  • Reviews
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

We present a survey of results on models of consensus in asynchronous multiagent systems with discrete and continuous time. We consider mathematical methods developed over recent years, which are used in the analysis of stability, stabilization, and consensus problems for linear multiagent systems with discrete time. These methods are based on the idea of using the notion of joint/generalized spectral radius of a set of matrices to analyze the rate of convergence of matrix products with factors drawn from certain sets of matrices with special properties.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bhaya, A., Kaszkurewicz, E., and Kozyakin, V.S., Existence and Stability of a Unique Equilibrium in Continuous–Valued Discrete–Time Asynchronous Hopfield Neural Networks, Proc. 1995 IEEE Int. Sympos. Circuits Syst., ISCAS’95, 1995, vol. 2, pp. 1140–1143.

    Google Scholar 

  2. Kozyakin, V.S., Bhaya, A., and Kaszkurewicz, E., A Global Asymptotic Stability Result for a Class of Totally Asynchronous Discrete Nonlinear Systems, Math. Control Signals Syst., 1999, vol. 12, no. 2, pp. 143–166.

    Article  MathSciNet  MATH  Google Scholar 

  3. MacKay, D.J.C., Information Theory, Inference and Learning Algorithms, New York: Cambridge Univ. Press, 2003, p. xii+628.

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  5. Proskurnikov, A.V. and Fradkov, A.L., Problems and Methods of Network Control, Autom. Remote Control, 2016, vol. 77, no. 10, pp. 1711–1740.

    Article  MathSciNet  MATH  Google Scholar 

  6. Szyld, D.B., The Mistery of Asynchronous Iterations Convergence When the Spectral Radius is One, Report 98–102, Temple University: College of Science and Technology, 1998. https://math.temple.edu/szyld/reports/mystery.pdf

    Google Scholar 

  7. Asarin, E.A., Kozyakin, V.S., Krasnosel’skii, M.A., and Kuznetsov, N.A., Analiz ustoichivosti rassinkhronizirovannykh diskretnykh sistem (Stability Analysis for Desynchronized Discrete Systems), Moscow: Nauka, 1992.

    Google Scholar 

  8. Bertsekas, D.P. and Tsitsiklis, J.N., Parallel and Distributed Computation. Numerical Methods, Englewood Cliffs: Prentice Hall, 1989.

    MATH  Google Scholar 

  9. Kozyakin, V., An Annotated Bibliography on Convergence of Matrix Products and the Theory of Joint/Generalized Spectral Radius, Moscow: Inst. for Information Transmission Problems, 2013. https://drive.google.com/uc?export=download&id=0Bxw63g5l4P7pLXgwcWxVZ3RoTVk

    Google Scholar 

  10. Sridharan, G., Srisailam, M.C., and Rao, V.S., A Note on the Effect of Asynchronous Sampling on Estimation Accuracy, Automatica, 1985, vol. 21, no. 4, pp. 491–493.

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  12. Fang, L. and Antsaklis, P.J., Information Consensus of Asynchronous Discrete–Time Multi–Agent Systems, Proc. 2005Am. Control Conf. (ACC), IEEE, 2005, pp. 1883–1888.

    Google Scholar 

  13. Zhu, W., Jiang, Z.P., and Feng, G., Event–Based Consensus of Multi–Agent Systems with General Linear Models, Automatica, 2014, vol. 50, no. 2, pp. 552–558.

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhu, W. and Jiang, Z.P., Event–Based Leader–Following Consensus of Multi–Agent Systems with Input Time Delay, IEEE Trans. Automat. Control, 2015, vol. 60, no. 5, pp. 1362–1367.

    Article  MathSciNet  MATH  Google Scholar 

  15. Hu, W., Liu, L., and Feng, G., Consensus of Linear Multi–Agent Systems by Distributed Event–Triggered Strategy, IEEE Trans. Cybernet., 2016, vol. 46, no. 1, pp. 148–157.

    Article  Google Scholar 

  16. Hu, W., Liu, L., and Feng, G., Output Consensus of Heterogeneous Linear Multi–Agent Systems by Distributed Event–Triggered/Self–Triggered Strategy, IEEE Trans. Cybernet., 2017, vol. 47, no. 8, pp. 1914–1924.

    Article  Google Scholar 

  17. Yang, D., Ren, W., Liu, X., and Chen, W., Decentralized Event–Triggered Consensus for Linear Multi–Agent Systems under General Directed Graphs, Automatica, 2016, vol. 69, pp. 242–249.

    Article  MathSciNet  MATH  Google Scholar 

  18. Guinaldo, M., Sánchez, J., and Dormido, S., Distributed Adaptive Control of Linear Multi–Agent Systems with Event–Triggered Communications, App. Math. Comput., 2016, vol. 274, pp. 195–207.

    Article  MathSciNet  MATH  Google Scholar 

  19. Ge, X., Han, Q.L., and Yang, F., Event–Based Set–Membership Leader–Following Consensus of Networked Multi–Agent Systems Subject to Limited Communication Resources and Unknown–but–Bounded Noise, IEEE Trans. Ind. Electron., 2017, vol. 64, no. 6, pp. 5045–5054.

    Article  Google Scholar 

  20. Xu, W., Ho, D.W., Li, L., and Cao, J., Event–Triggered Schemes on Leader–Following Consensus of General Linear Multiagent Systems under Different Topologies, IEEE Trans. Cybernet., 2017, vol. 47, no. 1, pp. 212–223.

    Article  Google Scholar 

  21. 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 

  22. Amelina, N., Fradkov, A., Jiang, Y., 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  MATH  Google Scholar 

  23. Ding, L. and Zheng, W.X., Consensus Tracking in Heterogeneous Nonlinear Multi–Agent Networks with Asynchronous Sampled–Data Communication, Syst. Control Lett., 2016, vol. 96, pp. 151–157.

    Article  MathSciNet  MATH  Google Scholar 

  24. Yin, X., Yue, D., and Hu, S., Adaptive Periodic Event–Triggered Consensus for Multi–Agent Systems Subject to Input Saturation, Int. J. Control, 2016, vol. 89, no. 4, pp. 653–667.

    Article  MathSciNet  MATH  Google Scholar 

  25. Xiao, F., Shi, Y., and Ren, W., Robustness Analysis of Asynchronous Sampled–Data Multiagent Networks with Time–Varying Delays, IEEE Trans. Automat. Control, 2018, vol. 63, no. 7.

    Google Scholar 

  26. Ge, X., Han, Q.L., Ding, D., Zhang, X.M., and Ning, B., A Survey on Recent Advances in Distributed Sampled–Data Cooperative Control of Multi–Agent Systems, Neurocomput., 2018, vol. 275, pp. 1684–1701.

    Article  Google Scholar 

  27. Gao, Y. and Wang, L., Sampled–Data Based Consensus of Continuous–Time Multi–Agent Systems with Time–Varying Topology, IEEE Trans. Automat. Control, 2011, vol. 56, no. 5, pp. 1226–1231.

    Article  MathSciNet  MATH  Google Scholar 

  28. Cao, M., Morse, A.S., and Anderson, B.D.O., Agreeing Asynchronously, IEEE Trans. Autom. Control, vol. 53, no. 8, pp. 1826–1838.

  29. Gao, Y. and Wang, L., Asynchronous Consensus of Continuous–Time Multi–Agent Systems with Intermittent Measurements, Int. J. Control, 2010, vol. 83, no. 3, pp. 552–562.

    Article  MathSciNet  MATH  Google Scholar 

  30. Meng, X. and Chen, T., Optimal Sampling and Performance Comparison of Periodic and Event Based Impulse Control, IEEE Trans. Automat. Control, 2012, vol. 57, no. 12, pp. 3252–3259.

    Article  MathSciNet  MATH  Google Scholar 

  31. Ge, X., Han, Q.L., and Jiang, X., Sampled–Data H∞ Filtering of Takagi–Sugeno Fuzzy Systems with Interval Time–Varying Delays, J. Franklin Inst., 2014, vol. 351, no. 5, pp. 2515–2542.

    Article  MathSciNet  MATH  Google Scholar 

  32. Ge, X. and Han, Q.L., Distributed Sampled–Data Asynchronous H∞ Filtering of Markovian Jump Linear Systems over Sensor Networks, Signal Proc., 2016, vol. 127, pp. 86–99.

    Article  Google Scholar 

  33. Marvasti, F., Nonuniform Sampling: Theory and Practice, Berlin: Springer–Verlag, 2001.

    Book  MATH  Google Scholar 

  34. Boyd, S., Ghosh, A., Prabhakar, B., and Shah, D., Randomized Gossip Algorithms, IEEE Trans. Inform. Theory, 2006, vol. 52, no. 6, pp. 2508–2530.

    Article  MathSciNet  MATH  Google Scholar 

  35. Proskurnikov, A.V. and Tempo, R., A Tutorial on Modeling and Analysis of Dynamic Social Networks. Part II, Annual Rev. Control, 2018, vol. 45, pp. 166–190.

    Article  MathSciNet  Google Scholar 

  36. Ellis, P., Extension of Phase Plane Analysis to Quantized Systems, IRE Trans. Automat. Control, 1959, vol. 4, no. 2, pp. 43–54.

    Article  Google Scholar 

  37. Pavlidis, T. and Jury, E., Analysis of a New Class of Pulse–Frequency Modulated Feedback Systems, IEEE Trans. Automat. Control, 1965, vol. 10, no. 1, pp. 35–43.

    Article  Google Scholar 

  38. Gelig, A.Kh. and Churilov, A.N., Kolebaniya i ustoichivost’ nelineinykh impul’snykh sistem (Oscillations and Stability of Nonlinear Impulse Systems), St. Petersburg: S.–Peterburg. Gos. Univ., 1993.

    Google Scholar 

  39. Åström, K.J. and Bernhardsson, B., Comparison of Periodic and Event Based Sampling for First–Order Stochastic Systems, IFAC Proc. Vol., 1999, vol. 32, no. 2, pp. 5006–5011.

    Article  Google Scholar 

  40. Åström, K.J. and Bernhardsson, B.M., Comparison of Riemann and Lebesgue Sampling for First Order Stochastic Systems, Proc. 41st IEEE Conf. Decision Control (CDC), 2002, IEEE, 2002, vol. 2, pp. 2011–2016.

    Article  Google Scholar 

  41. Tabuada, P., Event–Triggered Real–Time Scheduling of Stabilizing Control Tasks, IEEE Trans. Autom. Control, 2007, vol. 52, no. 9, pp. 1680–1685.

    Article  MathSciNet  MATH  Google Scholar 

  42. Anta, A. and Tabuada, P., To Sample or not to Sample: Self–Triggered Control for Nonlinear Systems, IEEE Trans. Automat. Control, 2010, vol. 55, no. 9, pp. 2030–2042.

    Article  MathSciNet  MATH  Google Scholar 

  43. Zhang, D., Han, Q.–L. and Jia, X., Network–Based Output Tracking Control for TCS Fuzzy Systems Using an Event–Triggered Communication Scheme, Fuzzy Sets Syst., 2015, vol. 273, pp. 26–48.

    Article  MATH  Google Scholar 

  44. Zhang, X.M. and Han, Q.L., A Decentralized Event–Triggered Dissipative Control Scheme for Systems with Multiple Sensors to Sample the System Outputs, IEEE Trans. Cybernet., 2016, vol. 46, no. 12, pp. 2745–2757.

    Article  Google Scholar 

  45. 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 

  46. Proskurnikov, A.V. and Cao, M., Synchronization of Pulse–Coupled Oscillators and Clocks under Minimal Connectivity Assumptions, IEEE Trans. Automat. Control, 2017, vol. 62, no. 11, pp. 5873–5879.

    Article  MathSciNet  MATH  Google Scholar 

  47. Heemels, W.P.M.H., Donkers, M.C.F., and Teel, A.R., Periodic Event–Triggered Control for Linear Systems, IEEE Trans. Automat. Control, 2013, vol. 58, no. 4, pp. 847–861.

    Article  MathSciNet  MATH  Google Scholar 

  48. Xiao, F. and Chen, T., Sampled–Data Consensus in Multi–Agent Systems with Asynchronous Hybrid Event–Time Driven Interactions, Syst. Control Lett., 2016, vol. 89, pp. 24–34.

    Article  MathSciNet  MATH  Google Scholar 

  49. Mikheev, Yu.V., Sobolev, V.A., and Fridman, É.M., Asymptotic Analysis of Digital Control Systems, Autom. Remote Control, 1988, vol. 49, no. 9, part 1, pp. 1175–1180.

    MATH  Google Scholar 

  50. Fridman, E., New Lyapunov–Krasovskii Functionals for Stability of Linear Retarded and Neutral Type Systems, Syst. Control Lett., 2001, vol. 43, no. 4, pp. 309–319.

    Article  MathSciNet  MATH  Google Scholar 

  51. Fridman, E. and Shaked, U., Delay–Dependent Stability and H∞ Control: Constant and Time–Varying Delays, Int. J. Control, 2003, vol. 76, no. 1, pp. 48–60.

    Article  MathSciNet  MATH  Google Scholar 

  52. Liu, K. and Fridman, E., Stability Analysis of Networked Control Systems: A Discontiuous Lyapunov Functional Approach, Proc. 48th IEEE Conf. Decision Control held jointly with the 28th Chinese Control Conf., CDC/CCC 2009, IEEE, 2009, pp. 1330–1335.

    Google Scholar 

  53. Hetel, L., Fiter, C., Omran, H., Seuret, A., Fridman, E., Richard, J.P., and Niculescu, S.I., Recent Developments on the Stability of Systems with Aperiodic Sampling: An Overview, Automatica, 2017, vol. 76, pp. 309–335.

    Article  MathSciNet  MATH  Google Scholar 

  54. Zhang, X.M. and Han, Q.L., Event–Triggered H∞ Control for a Class of Nonlinear Networked Control Systems Using Novel Integral Inequalities, Int. J. Robust Nonlin. Control, 2017, vol. 27, no. 4, pp. 679–700.

    Article  MathSciNet  MATH  Google Scholar 

  55. Ugrinovskii, V. and Fridman, E., A Round–Robin Type Protocol for Distributed Estimation with H∞ Consensus, Syst. Control Lett., 2014, vol. 69, pp. 103–110.

    Article  MathSciNet  MATH  Google Scholar 

  56. Zareh, M., Dimarogonas, D.V., Franceschelli, M., Johansson, K.H., and Seatzu, C., Consensus in Multi–Agent Systems with Non–Periodic Sampled–Data Exchange and Uncertain Network Topology, Int. Conf. Control, Decision and Inform. Technol. (CoDIT–2014), IEEE, 2014, pp. 411–416.

    Google Scholar 

  57. Song, Q., Liu, F., Wen, G., Cao, J., and Yang, X., Distributed Position–Based Consensus of Second–Order Multiagent Systems with Continuous/Intermittent Communication, IEEE Trans. Cybernet., 2017, vol. 47, no. 8, pp. 1860–1871.

    Article  Google Scholar 

  58. Wang, X., Wang, H., Li, C., Huang, T., and Kurths, J., Consensus Seeking in Multiagent Systems with Markovian Switching Topology under Aperiodic Sampled Data, IEEE Trans. Syst., Man, Cybernet.: Syst., 2018 (Early Access).

    Book  Google Scholar 

  59. Lin, J., Morse, A.S., and Anderson, B.D.O., The Multi–Agent Rendezvous Problem—the Asynchronous Case, 43rd IEEE Conf. Decision Control (CDC), 2004, IEEE, 2004, vol. 2, pp. 1926–1931.

    Google Scholar 

  60. Lin, J., Morse, A.S., and Anderson, B.D.O., The Multi–Agent Rendezvous Problem. Part 2: The Asynchronous Case, SIAM J. Control Optim., 2007, vol. 46, no. 6, pp. 2120–2147.

    Article  MathSciNet  MATH  Google Scholar 

  61. Tsitsiklis, J.N., Problems in Decentralized Decision Making and Computation, PhD. Dissertation, MIT, Cambridge, 1984.

    Google Scholar 

  62. Blondel, V.D., Hendrickx, J.M., Olshevsky, A., and Tsitsiklis, J.N., Convergence in Multiagent Coordination, Consensus, and Flocking, 44th IEEE Conf. Decision Control (CDC–ECC’05), IEEE, 2005, pp. 2996–3000.

    Google Scholar 

  63. Cao, M., Morse, A.S., and Anderson, B.D.O., Coordination of an Asynchronous Multi–Agent System via Averaging, IFAC Proc. Vol., 2005, vol. 38, no. 1, pp. 17–22.

    Article  Google Scholar 

  64. Sarymsakov, T.A., On the Ergodic Principle for Non–Uniform Markov Chains, Dokl. Akad. Nauk SSSR, 1953, vol. 90, no. 1, pp. 25–28.

    Google Scholar 

  65. Sarymsakov, T.A., On Non–Uniform Markov Chains, Dokl. Akad. Nauk SSSR, 1958, vol. 120, no. 3, pp. 465–467.

    MathSciNet  MATH  Google Scholar 

  66. Sarymsakov, T.A., Non–Uniform Markov Chains, Teor. Veroyatn. Primen., 1961, vol. 6, no. 2, pp. 194–201.

    Google Scholar 

  67. Hajnal, J. and Bartlett, M.S., The Ergodic Properties of Non–Homogeneous Finite Markov Chains, Math. Proc. Cambridge Philosoph. Soc., 1956, vol. 52, no. 1, pp. 67–77.

    Article  MathSciNet  MATH  Google Scholar 

  68. Hajnal, J. and Bartlett, M.S., Weak Ergodicity in Non–Homogeneous Markov Chains, Math. Proc. Cambridge Philosoph. Soc., 1958, vol. 54, no. 2, pp. 233–246.

    Article  MathSciNet  MATH  Google Scholar 

  69. Wolfowitz, J., Products of Indecomposable, Aperiodic, Stochastic Matrices, Proc. Am. Math. Soc., 1963, vol. 15, pp. 733–736.

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  71. Agaev, R.P. and Chebotarev, P.Yu., Convergence and Stability in Coordination Problems of Characteristics (Survey of Fundamental Results), Upravlen. Bol’shimi Sist., 2010, vol. 30, no. 1, pp. 470–505.

    Google Scholar 

  72. Di Fatta, G., Blasa, F., Cafiero, S., and Fortino, G., Fault Tolerant Decentralised k–Means Clustering for Asynchronous Large–Scale Networks, J. Parallel Distributed Comput., 2013, vol. 73, no. 3, pp. 317–329.

    Google Scholar 

  73. Lubachevsky, B. and Mitra, D., A Chaotic Asynchronous Algorithm for Computing the Fixed Point of a Nonnegative Matrix of Unit Spectral Radius, J. ACM (JACM), 1986, vol. 33, no. 1, pp. 130–150.

    Article  MathSciNet  MATH  Google Scholar 

  74. Moreau, L., Leaderless Coordination via Bidirectional and Unidirectional Time–Dependent Communication, Proc. 42nd IEEE Conf. Decision Control (CDC), 2003, IEEE, 2003, vol. 3, pp. 3070–3075.

    Google Scholar 

  75. Ren, W. and Beard, R.W., Consensus of Information under Dynamically Changing Interaction Topologies, Proc. 2004ACC, Boston, 2004, pp. 4939–4944.

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  78. Agaev, R.P. and Chebotarev, P.Yu., Spanning Forests of a Digraph and Their Applications, Autom. Remote Control, 2001, vol. 62, no. 3, pp. 443–466.

    Article  MathSciNet  MATH  Google Scholar 

  79. Chebotarev, P. and Agaev, R., Forest Matrices around the Laplacian Matrix, Linear Algebra Appl., 2002, vol. 356, pp. 253–274.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  81. Agaev, R.P. and Chebotarev, P.Yu., On Asymptotics in Consensus Models, Upravlen. Bol’shimi Sist., 2013, vol. 43, pp. 55–77.

    Google Scholar 

  82. Agaev, R.P. and Chebotarev, P.Yu., Coordination in Multiagent Systems and Laplacian Spectra of Digraphs, Autom. Remote Control, 2009, vol. 70, no. 3, pp. 469–483.

    Article  MathSciNet  MATH  Google Scholar 

  83. Chebotarev, P., Comments on “Consensus and Cooperation in Networked Multi–Agent Systems,” Proc. IEEE, 2010, vol. 98, no. 7, pp. 1353–1354.

    Google Scholar 

  84. Fang, L. and Antsaklis, P.J., Asynchronous Consensus Protocols Using Nonlinear Paracontractions Theory, IEEE Trans. Automat. Control, 2008, vol. 53, no. 10, pp. 2351–2355.

    Article  MathSciNet  MATH  Google Scholar 

  85. Qin, J., Yu, C., and Hirche, S., Stationary Consensus of Asynchronous Discrete–Time Second–Order Multi–Agent Systems under Switching Topology, IEEE Trans. Ind. Inform., 2012, vol. 8, no. 4, pp. 986–994.

    Article  Google Scholar 

  86. Qin, J., Gao, H., and Zheng, W.X., Consensus Strategy for a Class of Multi–Agents with Discrete Second–Order Dynamics, Int. J. Robust Nonlin. Control, 2012, vol. 22, no. 4, pp. 437–452.

    Article  MathSciNet  MATH  Google Scholar 

  87. Zhou, B., Liao, X., Huang, T., Wang, H., and Chen, G., Constrained Consensus of Asynchronous Discrete–Time Multi–Agent Systems with Time–Varying Topology, Inform. Sci., 2015, vol. 320, pp. 223–234.

    Article  MathSciNet  MATH  Google Scholar 

  88. Nedic, A., Ozdaglar, A., and Parrilo, P.A., Constrained Consensus and Optimization in Multi–Agent Networks, IEEE Trans. Automat. Control, 2010, vol. 55, no. 4, pp. 922–938.

    Article  MathSciNet  MATH  Google Scholar 

  89. Gubin, L.G., Polyak, B.T., and Raik, E.V., The Method of Projections for Finding Common Points of Convex Sets, Zh. Vychisl. Mat. Mat. Fiz., 1967, no. 7, pp. 1–24.

    Google Scholar 

  90. Shao, J., Shi, L., Zheng, W.X., and Huang, T.Z., Containment Control for Heterogeneous Multi–Agent Systems with Asynchronous Updates, Inform. Sci., 2018, vol. 436, pp. 74–88.

    Article  MathSciNet  Google Scholar 

  91. Shi, L., Shao, J., Cao, M., and Xia, H., Asynchronous Group Consensus for Discrete–Time Heterogeneous Multi–Agent Systems under Dynamically Changing Interaction Topologies, Inform. Sci., 2018, vol. 463–464, pp. 282–293.

    Article  MathSciNet  Google Scholar 

  92. Xiao, F. and Wang, L., Asynchronous Consensus in Continuous–Time Multi–Agent Systems with Switching Topology and Time–Varying Delays, IEEE Trans. Autom. Control, 2008, vol. 53, no. 8, pp. 1804–1816.

    Article  MathSciNet  MATH  Google Scholar 

  93. Almeida, J., Silvestre, C., and Pascoal, A.M., Continuous–Time Consensus with Discrete–Time Communications, Syst. Control Lett., 2012, vol. 61, no. 7, pp. 788–796.

    Article  MathSciNet  MATH  Google Scholar 

  94. Xiao, F. and Chen, T., Sampled–Data Consensus for Multiple Double Integrators with Arbitrary Sampling, IEEE Trans. Autom. Control, 2012, vol. 57, no. 12, pp. 3230–3235.

    Article  MathSciNet  MATH  Google Scholar 

  95. Zhan, J. and Li, X., Asynchronous Consensus of Multiple Double–Integrator Agents with Arbitrary Sampling Intervals and Communication Delays, IEEE Trans. Circuits Syst. I: Regular Papers, 2015, vol. 62, no. 9, pp. 2301–2311.

    Article  MathSciNet  Google Scholar 

  96. Jiang, F., Liu, B., Wu, Y., and Zhu, Y., Asynchronous Consensus of Second–OrderMulti–Agent Systems with Impulsive Control and Measurement Time–Delays, Neurocomput., 2018, vol. 275, pp. 932–939.

    Article  Google Scholar 

  97. Liu, Z.W., Guan, Z.H., Shen, X., and Feng, G., Consensus of Multi–Agent Networks with Aperiodic Sampled Communication via Impulsive Algorithms Using Position–Only Measurements, IEEE Trans. Automat. Control, 2012, vol. 57, no. 10, pp. 2639–2643.

    Article  MathSciNet  MATH  Google Scholar 

  98. Ding, D., Wang, Z., Shen, B., and Wei, G., Event–Triggered Consensus Control for Discrete–Time Stochastic Multi–Agent Systems: The Input–to–State Stability in Probability, Automatica, 2015, vol. 62, pp. 284–291.

    Article  MathSciNet  MATH  Google Scholar 

  99. Ma, L., Wang, Z., and Lam, H.K., Event–Triggered Mean–Square Consensus Control for Time–Varying Stochastic Multi–Agent System with Sensor Saturations, IEEE Trans. Automat. Control, 2017, vol. 62, no. 7, pp. 3524–3531.

    Article  MathSciNet  MATH  Google Scholar 

  100. Dashkovskiy, S.N., Efimov, D.V., and Sontag, E.D., Input to State Stability and Allied System Properties, Autom. Remote Control, 2011, vol. 72, no. 8, pp. 1579–1614.

    Article  MathSciNet  MATH  Google Scholar 

  101. Ding, D., Wang, Z., Ho, D.W., and Wei, G., Observer–Based Event–Triggering Consensus Control for Multiagent Systems with Lossy Sensors and Cyber–Attacks, IEEE Trans. Cybernet., 2017, vol. 47, no. 8, pp. 1936–1947.

    Article  Google Scholar 

  102. Seyboth, G.S., Dimarogonas, D.V., and Johansson, K.H., Event–Based Broadcasting for Multi–Agent Average Consensus, Automatica, 2013, vol. 49, no. 1, pp. 245–252.

    Article  MathSciNet  MATH  Google Scholar 

  103. Dimarogonas, D.V., Frazzoli, E., and Johansson, K.H., Distributed Event–Triggered Control for Multi–Agent Systems, IEEE Trans. Automat. Control, 2012, vol. 57, no. 5, pp. 1291–1297.

    Article  MathSciNet  MATH  Google Scholar 

  104. Yi, X., Lu, W., and Chen, T., Pull–Based Distributed Event–Triggered Consensus for Multiagent Systems with Directed Topologies, IEEE Trans. Neural Netw. Learning Syst., 2017, vol. 28, no. 1, pp. 71–79.

    Article  MathSciNet  Google Scholar 

  105. Fan, Y., Feng, G.,Wang, Y., and Song, C., Distributed Event–TriggeredControl ofMulti–Agent Systems with Combinational Measurements, Automatica, 2013, vol. 49, no. 2, pp. 671–675.

    Google Scholar 

  106. Garcia, E., Cao, Y., Yu, H., Antsaklis, P., and Casbeer, D., Decentralised Event–Triggered Cooperative Control with Limited Communication, Int. J. Control, 2013, vol. 86, no. 9, pp. 1479–1488.

    Article  MathSciNet  MATH  Google Scholar 

  107. Chen, X., Hao, F., and Shao, M., Event–Triggered Consensus of Multi–Agent Systems under Jointly Connected Topology, IMA J. Math. Control Inform., 2015, vol. 32, no. 3, pp. 537–556.

    Article  MathSciNet  MATH  Google Scholar 

  108. Wang, X., Su, H., Wang, X., and Chen, G., Fully Distributed Event–Triggered Semiglobal Consensus of Multi–Agent Systems with Input Saturation, IEEE Trans. Ind. Electron., 2017, vol. 64, no. 6, pp. 5055–5064.

    Article  Google Scholar 

  109. Mu, N., Liao, X., and Huang, T., Event–Based Consensus Control for a Linear Directed Multiagent System with Time Delay, IEEE Trans. Circuits Syst. II: Express Briefs, 2015, vol. 62, no. 3, pp. 281–285.

    Article  Google Scholar 

  110. Zhu, W., Pu, H., Wang, D., and Li, H., Event–Based Consensus of Second–Order Multi–Agent Systems with Discrete Time, Automatica, 2017, vol. 79, pp. 78–83.

    Article  MathSciNet  MATH  Google Scholar 

  111. Nowzari, C. and Pappas, G.J., Multi–Agent Coordination with Asynchronous Cloud Access, Am. Control Conf. (ACC), 2016, IEEE, 2016, pp. 4649–4654.

    Google Scholar 

  112. Yue, D., Tian, E., and Han, Q.L., A Delay System Method for Designing Event–Triggered Controllers of Networked Control Systems, IEEE Trans. Automat. Control, 2013, vol. 58, no. 2, pp. 475–481.

    Article  MathSciNet  MATH  Google Scholar 

  113. Peng, C. and Han, Q.–L., On Designing a Novel Self–Triggered Sampling Scheme for Networked Control Systems with Data Losses and Communication Delays, IEEE Trans. Ind. Electron., 2016, vol. 63, no. 2, pp. 1239–1248.

    Article  Google Scholar 

  114. Li, H., Chen, Z., Wu, L., and Lam, H.K., Event–Triggered Control for Nonlinear Systems under Unreliable Communication Links, IEEE Trans. Fuzzy Syst., 2017, vol. 25, no. 4, pp. 813–824.

    Article  Google Scholar 

  115. Zhang, X.M., Han, Q.L., and Yu, X., Survey on Recent Advances in Networked Control Systems, IEEE Trans. Ind. Inform., 2016, vol. 12, no. 5, pp. 1740–1752.

    Article  Google Scholar 

  116. Zhang, X.M., Han, Q.L., and Zhang, B.L., An Overview and Deep Investigation on Sampled–Data–Based Event–Triggered Control and Filtering for Networked Systems, IEEE Trans. Ind. Inform., 2017, vol. 13, no. 1, pp. 4–16.

    Article  MathSciNet  Google Scholar 

  117. Cheng, Y. and Ugrinovskii, V., Event–Triggered Leader–Following Tracking Control for Multivariable Multi–Agent Systems, Automatica, 2016, vol. 70, pp. 204–210.

    Article  MathSciNet  MATH  Google Scholar 

  118. Xie, T., Liao, X., and Li, H., Leader–Following Consensus in Second–Order Multi–Agent Systems with Input Time Delay: An Event–Triggered Sampling Approach, Neurocomput., 2016, vol. 177, pp. 130–135.

    Article  Google Scholar 

  119. Cook, P.A., Describing Function for a Sector Nonlinearity, Proc. Inst. Electrical Engineers, 1973, vol. 120, no. 1, pp. 143–144.

    Article  Google Scholar 

  120. Fradkov, A.L. and Seifullaev, R.E., Discretization of Control Systems, Proc. Intl. Chetaev Conf. Analytic Mechanics, Stability, and Control: Plenary Talks, Kazan, June 13–17, 2017, Kazan: KNITU–KAI, 2017, pp. 186–193.

    Google Scholar 

  121. Gao, H., Wu, J., and Shi, P., Robust Sampled–Data H∞ Control with Stochastic Sampling, Automatica, 2009, vol. 45, no. 7, pp. 1729–1736.

    Article  MathSciNet  MATH  Google Scholar 

  122. Zhang, X.M. and Han, Q.L., New Lyapunov–Krasovskii Functionals for Global Asymptotic Stability of Delayed Neural Networks, IEEE Trans. Neural Networks, 2009, vol. 20, no. 3, pp. 533–539.

    Article  Google Scholar 

  123. Zhang, X.M. and Han, Q.L., Global Asymptotic Stability Analysis for Delayed Neural Networks Using a Matrix–Based Quadratic Convex Approach, Neural Networks, 2014, vol. 54, pp. 57–69.

    Article  MATH  Google Scholar 

  124. Wu, X., Tang, Y., Cao, J., and Zhang, W., Distributed Consensus of Stochastic Delayed Multi–Agent Systems under Asynchronous Switching, IEEE Trans. Cybernet., 2016, vol. 46, no. 8, pp. 1817–1827.

    Article  Google Scholar 

  125. Yang, Z. and Xu, D., Stability Analysis and Design of Impulsive Control Systems with Time Delay, IEEE Trans. Automat. Control, 2007, vol. 52, no. 8, pp. 1448–1454.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    V. S. Kozyakin

  2. Kotelnikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow, Russia

    V. S. Kozyakin, N. A. Kuznetsov & P. Yu. Chebotarev

  3. Moscow Institute of Physics and Technology, Moscow, Russia

    N. A. Kuznetsov & P. Yu. Chebotarev

  4. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    P. Yu. Chebotarev

Authors
  1. V. S. Kozyakin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. A. Kuznetsov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Yu. Chebotarev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to V. S. Kozyakin, N. A. Kuznetsov or P. Yu. Chebotarev.

Additional information

Russian Text © V.S. Kozyakin, N.A. Kuznetsov, P.Yu. Chebotarev, 2019, published in Avtomatika i Telemekhanika, 2019, No. 4, pp. 3–40.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kozyakin, V.S., Kuznetsov, N.A. & Chebotarev, P.Y. Consensus in Asynchronous Multiagent Systems. I. Asynchronous Consensus Models. Autom Remote Control 80, 593–623 (2019). https://doi.org/10.1134/S0005117919040015

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117919040015

Keywords

Search

Navigation