Skip to main content
SpringerLink
Log in

Consensus control of stochastic multi-agent systems: a survey

  • Review
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

In this article, we provide a review of the consensus control problem for stochastic multi-agent systems (MASs). Recent advances are surveyed according to the method of occurrence of the stochasticity of the MASs. First, the consensus problem is discussed for MASs, wherein individual agents are corrupted by random noises, i.e., the dynamics of agents involve stochasticity in process and/or measurement equations. Both additive noises and multiplicative noises are surveyed in detail and special attention is paid to the MASs whose dynamics are governed by Itô differential equations. Moreover, particular effort is devoted to presenting the latest progress on the consensus problem for a special type of stochastic MAS with Markovian jump parameters. Subsequently, the relevant research is summarized for MASs with noisy communication environments and stochastic sampling. Further, we provide a systematic review of the consensus problems for MASs whose communication topology varies randomly in the process of data propagation among agents. Finally, conclusions are drawn and several potential future research directions are outlined.

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. Langbort C, Chandra R S, Andrea R D. Distributed control design for systems interconnected over an arbitrary graph. IEEE Trans Automat Contr, 2004, 49: 1502–1519

    Article  MATH  MathSciNet  Google Scholar 

  2. Gupta V, Hassibi B, Murray R M. A sub-optimal algorithm to synthesize control laws for a network of dynamic agents. Int J Control, 2005, 78: 1302–1313

    Article  MATH  MathSciNet  Google Scholar 

  3. Dunbar W B. Distributed receding horizon control of dynamically coupled nonlinear systems. IEEE Trans Automat Contr, 2007, 52: 1249–1263

    Article  MATH  MathSciNet  Google Scholar 

  4. Franco E, Magni L, Parisini T, et al. Cooperative constrained control of distributed agents with nonlinear dynamics and delayed information exchange: a stabilizing receding-horizon approach. IEEE Trans Automat Contr, 2008, 53: 324–338

    Article  MATH  MathSciNet  Google Scholar 

  5. Azuma Y, Ohtsuka T. Receding horizon Nash game approach for distributed nonlinear control. In: SICE Annual Conference, Tokyo, 2011. 380–384

    Google Scholar 

  6. Wang Z D, Ding D R, Dong H L, et al. H ∞ consensus control for multi-agent systems with missing measurements: the finite-horizon case. Syst Control Lett, 2013, 62: 827–836

    Article  MATH  MathSciNet  Google Scholar 

  7. Ming P S, Liu J C, Tan S B, et al. Consensus stabilization in stochastic multi-agent systems with Markovian switching topology, noises and delay. Neurocomputing, 2016, 200: 1–10

    Article  Google Scholar 

  8. Morita R, Wada T, Masubuchi I, et al. Time averaging algorithms with stopping rules for multi-agent consensus with noisy measurements. Asian J Control, 2016, 18: 1969–1982

    Article  MATH  MathSciNet  Google Scholar 

  9. Ma C Q, Qin Z Y. Bipartite consensus on networks of agents with antagonistic interactions and measurement noises. IET Control Theory A, 2016, 10: 2306–2313

    Article  MathSciNet  Google Scholar 

  10. Ma L F, Wang Z D, Lam H K. Event-triggered mean-square consensus control for time-varying stochastic multi-agent system with sensor saturations. IEEE Trans Automat Contr, 2017, 62: 3524–3531

    Article  MATH  MathSciNet  Google Scholar 

  11. Ma L F, Wang Z D, Lam H K. Mean-square H ∞ consensus control for a class of nonlinear time-varying stochastic multiagent systems: the finite-horizon case. IEEE Trans Syst Man Cybern Syst, 2017, 47: 1050–1060

    Article  Google Scholar 

  12. Andrea R, Dullerud G. Distributed control design for spatially interconnected systems. IEEE Trans Automat Contr, 2003, 48: 1478–1495

    Article  MATH  MathSciNet  Google Scholar 

  13. Ren W, Moore K, Chen Y Q. High-order consensus algorithms in cooperative vehicle systems. In: Proceedings of the 2006 IEEE International Conference on Networking, Sensing and Control, Fort Lauderdale, 2006. 457–462

    Google Scholar 

  14. Fax J A, Murray R M. Information flow and cooperative control of vehicle formations. IEEE Trans Automat Contr, 2004, 49: 1465–1476

    Article  MATH  MathSciNet  Google Scholar 

  15. Ge X H, Han Q L. Distributed formation control of networked multi-agent systems using a dynamic event-triggered communication mechanism. IEEE Trans Ind Electron, 2017, 64: 8118–8127

    Article  Google Scholar 

  16. Olfati-Saber R. Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans Automat Contr, 2016, 51: 401–420

    Article  MATH  MathSciNet  Google Scholar 

  17. Ding D R, Wang Z D, Shen B, et al. Event-triggered distributed H ∞ state estimation with packet dropouts through sensor networks. IET Control Theory A, 2015, 9: 1948–1955

    Article  MathSciNet  Google Scholar 

  18. Dong H L, Wang Z D, Gao H J. Distributed H ∞ filtering for a class of Markovian jump nonlinear time-delay systems over lossy sensor networks. IEEE Trans Ind Electron, 2013, 60: 4665–4672

    Article  Google Scholar 

  19. Ge X H, Han Q L. Distributed sampled-data asynchronous H ∞ filtering of Markovian jump linear systems over sensor networks. Signal Process, 2016, 127: 86–99

    Article  Google Scholar 

  20. Ge X H, Han Q L. Distributed event-triggered H ∞ filtering over sensor networks with communication delays. Inform Sci, 2015, 291: 128–142

    Article  MATH  MathSciNet  Google Scholar 

  21. Shen B, Wang Z D, Liu X H. A stochastic sampled-data approach to distributed H ∞ filtering in sensor networks. IEEE Trans Circuits-I, 2011, 58: 2237–2246

    Article  MathSciNet  Google Scholar 

  22. Ugrinovskii V. Distributed robust estimation over randomly switching networks using H ∞ consensus. Automatica, 2013, 49: 160–168

    Article  MATH  MathSciNet  Google Scholar 

  23. Toshiyuki Y, Nakatani S, Adachi A, et al. Adaptive role assignment for self-organized flocking of a real robotic swarm. Artif Life Robot, 2016, 21: 405–410

    Article  Google Scholar 

  24. Li W Y, Wei G L, Han F, et al. Weighted average consensus-based unscented Kalman filtering. IEEE Trans Cybern, 2016, 46: 558–567

    Article  Google Scholar 

  25. Olfati-Saber R, Shamma J S. Consensus filters for sensor networks and distributed sensor fusion. In: Proceedings of the 44th IEEE Conference on Decision and Control and 2005 European Control Conference, Seville, 2005. 6698–6703

    Google Scholar 

  26. Yuan Y, Sun F C. Data fusion-based resilient control system under DoS attacks: a game theoretic approach. Int J Control Automat Syst, 2015, 13: 513–520

    Article  Google Scholar 

  27. Hatano Y, Mesbahi M. Agreement over random networks. IEEE Trans Automat Contr, 2005, 50: 1867–1872

    Article  MATH  MathSciNet  Google Scholar 

  28. Jadbabaie A, Motee N, Barahona M. On the stability of the Kuramoto model of coupled nonlinear oscillators. In: Proceedings of the American Control Conference, Boston, 2004. 4296–4301

    Google Scholar 

  29. Xu Y, Lu R Q, Peng H, et al. Asynchronous dissipative state estimation for stochastic complex networks with quantized jumping coupling and uncertain measurements. IEEE Trans Neural Netw, 2017, 28: 268–277

    Article  MathSciNet  Google Scholar 

  30. Olfati-Saber R. Ultrafast consensus in small-world networks. In: Proceedings of the 2005 American Control Conference, Portland, 2005. 2372–2378

    Google Scholar 

  31. Yuan Y, Sun F C. Delay-dependent stability criteria for time-varying delay neural networks in the delta domain. Neurocomputing, 2013, 125: 17–21

    Article  Google Scholar 

  32. Fang L, Antsaklis P J, Tzimas A. Asynchronous consensus protocols: preliminary results, simulations and open questions. In: Proceedings of the 44th IEEE Conference on Decision and Control and 2005 European Control Conference, Seville, 2005. 2194–2199

    Google Scholar 

  33. Tron R, Thomas J, Loianno G, et al. A distributed optimization framework for localization and formation control: applications to vision-based measurements. IEEE Contr Syst Mag, 2016, 36: 22–44

    Article  MathSciNet  Google Scholar 

  34. Lu Q, Han Q L, Zhang B T, et al. Cooperative control of mobile sensor networks for environmental monitoring: an event-triggered finite-time control scheme. IEEE Trans Cybern, 2016, doi: 10.1109/TCYB.2016.2601110

    Google Scholar 

  35. Sakthivel R, Mohanapriya S, Karimi H R, et al. A robust repetitive-control design for a class of uncertain stochastic dynamical systems. IEEE Trans Circuits-II, 2017, 64: 427–431

    Google Scholar 

  36. Poznyak A S. Sliding mode control in stochastic continuos-time systems: μ-zone MS-convergence. IEEE Trans Automat Contr, 2017, 62: 863–868

    Article  MATH  MathSciNet  Google Scholar 

  37. Sahoo A, Jagannathan S. Stochastic optimal regulation of nonlinear networked control systems by using event-driven adaptive dynamic programming. IEEE Trans Cybern, 2017, 47: 425–438

    Google Scholar 

  38. Satoh S, Kappen H J, Saeki M. An iterative method for nonlinear stochastic optimal control based on path integrals. IEEE Trans Automat Contr, 2017, 62: 262–276.

    Article  MATH  MathSciNet  Google Scholar 

  39. Komaee A, Barton P I. Potential canals for control of nonlinear stochastic systems in the absence of state measurements. IEEE Trans Contr Syst Technol, 2017, 25: 161–174

    Article  Google Scholar 

  40. Mesbah A. Stochastic model predictive control: an overview and prespecitve for future research. IEEE Contr Syst Mag, 2016, 36: 30–44

    Article  Google Scholar 

  41. Abdollahi F, Khorasani K. A decentralized Markovian jump H ∞ control routing strategy for mobile multi-agent networked systems. IEEE Trans Contr Syst Technol, 2011, 19: 269–283

    Article  Google Scholar 

  42. Ge X H, Han Q L. Consensus of multi-agent systems subject to partially accessible and overlapping Markovian network topologies. IEEE Trans Cybern, 2017, 47: 1807–1819

    Article  Google Scholar 

  43. Meskin N, Khorasani K. Fault detection and isolation of discrete-time Markovian jump linear systems with application to a network of multi-agent systems having imperfect communication channels. Automatica, 2009, 45: 2032–2040

    Article  MATH  MathSciNet  Google Scholar 

  44. Mu X W, Zheng B J, Liu K. L 2−L ∞ containment control of multi-agent systems with Markovian switching topologies and non-uniform time-varying delays. IET Control Theory A, 2014, 8: 863–872

    Article  MathSciNet  Google Scholar 

  45. Ge X H, Han Q L, Yang F W. 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, 64: 5045–5054

    Article  Google Scholar 

  46. Fanaswala M, Krishnamurthy V. Detection of anomalous trajectory patterns in target tracking via stochastic context-free grammars and reciprocal process models. IEEE J Sel Top Signal Process, 2013, 7: 76–90

    Article  Google Scholar 

  47. Brinatti V, Guilermo D, Eduardo O, et al. Distributed temperature sensing using cyclic pseudorandom sequences. IEEE Sens J, 2017, 17: 1686–1691

    Article  Google Scholar 

  48. Cho Y, Park D. Sequential detector design for spectrum sensing considering instantaneously nonidentically distributed samples. IEEE Trans Veh Technol, 2017, 66: 2158–2169

    Article  Google Scholar 

  49. Cabell R, Palumbo D, Vipperman J. A principal component feedforward algorithm for active noise control: flight test results. IEEE Trans Contr Syst Technol, 2001, 9: 76–83

    Article  Google Scholar 

  50. Boukhnifer M, Chaibet A. Robust control of aerial vehicle flight: simulation and experimental results. IEEE Aerosp Electron Syst Mag, 2014, 29: 4–12

    Article  Google Scholar 

  51. Hafez A T, Marasco A J, Givigi S N, et al. Solving multi-UAV dynamic encirclement via model predictive control. IEEE Trans Contr Syst Technol, 2015, 23: 2251–2265

    Article  Google Scholar 

  52. Zhao B, Xian B, Zhang Y, et al. Nonlinear robust adaptive tracking control of a quadrotor UAV via immersion and invariance methodology. IEEE Trans Ind Electron, 2015, 62: 2891–2902

    Article  Google Scholar 

  53. Broek B, Wiegerinck W, Kappen B. Graphical model inference in optimal control of stochastic multi-agent systems. J Artif Intell Res, 2008, 32: 95–122

    MATH  Google Scholar 

  54. Zhang Q, Zhang J F. Adaptive tracking games for coupled stochastic linear multi-agent systems: stability, optimality and robustness. IEEE Trans Automat Contr, 2013, 58: 2862–2877

    Article  MATH  MathSciNet  Google Scholar 

  55. Zheng Y S, Chen W S, Wang L. Finite-time consensus for stochastic multi-agent systems. Int J Control, 2011, 84: 1644–1652

    Article  MATH  MathSciNet  Google Scholar 

  56. Ding D R, Wang Z D, Shen B, et al. Event-triggered consensus for discrete-time stochastic multi-agent systems: the input-to-state stability in probability. Automatica, 2015, 62: 284–291

    Article  MATH  MathSciNet  Google Scholar 

  57. Tang Y, Gao H J, Zhang W B, et al. Leader-following consensus of a class of stochastic delayed multi-agent systems with partial mixed impulses. Automatica, 2015, 53: 346–354

    Article  MATH  MathSciNet  Google Scholar 

  58. Feng Z, Hu G Q. Passivity-based consensus and passication for a class of stochastic multi-agent systems with switching topology. In: Proceedings of the 12th International Conference on Control, Automation, Robotics & Vision, Guangzhou, 2012. 1460–1465

    Google Scholar 

  59. Zhao L, Jia Y M. Finite-time consensus for second-order stochastic multi-agent systems with nonlinear dynamics. Appl Math Comput, 2015, 270: 278–290

    MathSciNet  Google Scholar 

  60. Li W, Zhou H, Liu Z W, et al. Impulsive coordination of nonlinear multi-agent systems with multiple leaders and stochastic disturbance. Neurocomputing, 2016, 171: 73–81

    Article  Google Scholar 

  61. Zhang B, He W L. Sampled-data consensus of nonlinear multi-agent systems with stochastic disturbances. In: Proceedings of the 41st Annual Conference of the IEEE Industrial Electronics Society, Yokohama, 2015. 2207–2212

    Google Scholar 

  62. Wu X T, Tang Y, Cao J D, et al. Distributed consensus of stochastic delayed multi-agent systems under asynchronous switching. IEEE Trans Cybern, 2016, 46: 1817–1827

    Article  Google Scholar 

  63. Wu X T, Tang Y, Zhang W B. Stability analysis of stochastic delayed systems with an application to multi-agent systems. IEEE Trans Automat Contr, 2016, 61: 4143–4149

    Article  Google Scholar 

  64. Dong H L, Wang Z D, Gao H J. Fault detection for Markovian jump systems with sensor saturations and randomly varying nonlinearities. IEEE Trans Circuits-I, 2012, 59: 2354–2362

    Article  MathSciNet  Google Scholar 

  65. Karimi H R. Robust delay-dependent H ∞ control of uncertain time-delay systems with mixed neutral, discrete, and distributed time-delays and Markovian switching parameters. IEEE Trans Circuits-I, 2011, 58: 1910–1923

    Article  MathSciNet  Google Scholar 

  66. Karimi H R. A sliding mode approach to H ∞ synchronization of master-slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties. J Franklin I, 2012, 349: 1480–1496

    Article  MATH  MathSciNet  Google Scholar 

  67. Karimi H R. Passivity-based output feedback control of Markovian jump systems with discrete and distributed time-varying delays. Int J Syst Sci, 2013, 44: 1290–1300

    Article  MATH  MathSciNet  Google Scholar 

  68. Li Q, Shen B, Liu Y R, et al. Event-triggered H ∞ state estimation for discrete-time stochastic genetic regulatory networks with Markovian jumping parameters and time-varying delays. Neurocomputing, 2016, 174: 912–920

    Article  Google Scholar 

  69. Liu Y R, Liu W B, Obaid M A, et al. Exponential stability of Markovian jumping Cohen-Grossberg neural networks with mixed mode-dependent time-delays. Neurocomputing, 2016, 177: 409–415

    Article  Google Scholar 

  70. Ma L F, Wang Z D, Bo Y M, et al. Finite-horizon H 2/H ∞ control for a class of nonlinear Markovian jump systems with probabilistic sensor failures. Int J Control, 2011, 84: 1847–1857

    Article  MATH  MathSciNet  Google Scholar 

  71. Sheng L, Zhang W H, Gao M. Relationship between Nash equilibrium strategies and H 2/H ∞ control of stochastic Markov jump systems with multiplicative noises. IEEE Trans Automat Contr, 2014, 59: 2592–2597

    Article  MATH  MathSciNet  Google Scholar 

  72. Terra M H, Ishihara J Y, Jesus G. Robust estimation for discrete-time Markovian jump linear systems. IEEE Trans Automat Contr, 2013, 58: 2065–2071

    Article  MATH  MathSciNet  Google Scholar 

  73. Wang B C, Zhang J F. Distributed output feedback control of Markov jump multi-agent systems. Automatica, 2013, 49: 1397–1402

    Article  MATH  MathSciNet  Google Scholar 

  74. Zhu S Y, Chen C L, Guan X P. Consensus protocol for heterogeneous multi-agent systems: a Markov chain approach. Chin Phys B, 2013, 22: 018901

    Article  Google Scholar 

  75. Azuma S, Baba I, Sugie T. Broadcast control of Markovian multi-agent systems. SICE J Control Meas Syst Integr, 2016, 9: 130–112

    Google Scholar 

  76. Mu X W, Zheng B J. Containment control of second-order discrete-time multi-agent systems with Markovian missing data. IET Control Theory A, 2015, 9: 1229–1237

    Article  MathSciNet  Google Scholar 

  77. Hou B, Sun F C, Li H B, et al. Stationary and dynamic consensus of second-order multi-agent systems with Markov jumping input delays. IET Control Theory A, 2004, 8: 1905–1913

    Article  MathSciNet  Google Scholar 

  78. Yi J W, Wang Y W, Xiao J W, et al. Consensus in second-order Markovian jump multi-agent systems via impulsive control using sampled information with heterogenous delays. Asian J Control, 2016, 18: 1940–1949

    Article  MATH  MathSciNet  Google Scholar 

  79. Yi J W, Wang Y W, Xiao J W. Consensus in Markovian jump second-order multi-agent systems with random communication delay. IET Control Theory A, 2014, 8: 1666–1675

    Article  MathSciNet  Google Scholar 

  80. Hu Y B, Lam J, Liang J L. Consensus control of multi-agent systems with missing data in actuators and Markovian communication failure. Int J Syst Sci, 2013, 44: 1867–1878

    Article  MATH  MathSciNet  Google Scholar 

  81. Park M J, Kwon O M, Park J H, et al. Randomly changing leader-following consensus control for Markovian switching multi-agent systems with interval time-varying delays. Nonlinear Anal-Hybr Syst, 2014, 12: 117–131

    Article  MATH  MathSciNet  Google Scholar 

  82. Huang M Y, Manton J. Coordination and consensus of networked agents with noisy measurements: stochastic algorithms and ssymptotic behavior. SIAM J Control Optim, 2009, 48: 134–161

    Article  MATH  MathSciNet  Google Scholar 

  83. Kar S, Moura J M F. Distributed consensus algorithms in sensor networks with imperfect communication: link failures and channel noise. IEEE Trans Signal Process, 2009, 57: 355–369

    Article  MathSciNet  Google Scholar 

  84. Li T, Zhang J F. Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises. IEEE Trans Automat Contr, 2010, 55: 2043–2057

    Article  MATH  MathSciNet  Google Scholar 

  85. Liu J, Zhang H T, Liu X Z, et al. Distributed stochastic consensus of multi-agent systems with noise and delayed measurements. IET Control Theory A, 2013, 7: 1359–1369

    Article  Google Scholar 

  86. Liu J, Liu X Z, Xie W C, et al. Stochastic consensus seeking with communication delays. Automatica, 2011, 47: 2689–2696

    Article  MATH  MathSciNet  Google Scholar 

  87. Li T, Zhang J F. Mean square average consensus under measurement noises and fixed topologies: necessary and sufficient conditions. Automatica, 2009, 45: 1929–1936

    Article  MATH  MathSciNet  Google Scholar 

  88. Zong X F, Li T, Zhang J F. Stochastic consensus of continuous time multi-agent systems with additive measurement noises. In: Proceedings of IEEE 54th Annual Conference on Decision and Control, Osaka, 2015. 543–548

    Google Scholar 

  89. Amelina N, Fradkov A. Approximate consensus in multi-agent nonlinear stochastic systems. In: Proceedings of European Control Conference (ECC), Strasbourg, 2014. 2833–2838

    Google Scholar 

  90. Robbins H, Monro S. A stochastic approximation method. Ann Math Stat, 1951, 22: 400–407

    Article  MATH  MathSciNet  Google Scholar 

  91. Chen H F. Stochastic Approximation and Its Applications. New York: Springer, 2002

    MATH  Google Scholar 

  92. Kushner H J, Yin G. Stochastic Approximation and Recursive Algorithms and Applications. New York: Springer. 2003

    MATH  Google Scholar 

  93. Spall J C. Introduction to Stochastic Search and Optimization. Hoboken: John Wiley & Sons, 2003

    Book  MATH  Google Scholar 

  94. Morita R, Wada T, Masubuchi I, et al. Multiagent consensus with noisy communication: stopping rules based on network graphs. IEEE Trans Contr Netw Syst, 2016, 3: 358–365

    Article  MATH  MathSciNet  Google Scholar 

  95. Zong X F, Li T, Zhang J F. Stochastic consensus of linear multi-agent systems with multiplicative measurement noises. In: Proceedings of the 12th IEEE International Conference on Control & Automation, Kathmandu, 2016. 7–12

    Google Scholar 

  96. Liu J C, Ming P S, Li S H. Consensus gain conditions of stochastic multi-agent system with communication noise. Int J Control Automat, 2016, 14: 1223–1230

    Article  Google Scholar 

  97. Schenato L, Firrentin F. Average TimeSynch: a consensus-based protocol for clock synchronization in wireless sensor networks. Automatica, 2011, 47: 1878–1886

    Article  MATH  MathSciNet  Google Scholar 

  98. Wu J, Shi Y. Consensus in multi-agent systems with random delays governed by a Markov chain. Syst Control Lett, 2011, 60: 863–870

    Article  MATH  MathSciNet  Google Scholar 

  99. Yin X X, Yue D. Event-triggered tracking control for heterogeneous multi-agent systems with Markov communication delays. J Franklin I, 2013, 350: 1312–1334

    Article  MATH  MathSciNet  Google Scholar 

  100. Tian Y P, Zhong S H, Cao Q Q. Structural modeling and convergence analysis of consensus-based time synchronization algorithms over networks: non-topological conditions. Automatica, 2016, 65: 64–75

    Article  MATH  MathSciNet  Google Scholar 

  101. Wang J, Elia N. Mitigation of complex behavior over networked systems: analysis of spatially invariant structures. Automatica, 2013, 49: 1626–1638

    Article  MATH  MathSciNet  Google Scholar 

  102. Ni W, Zhao D Y, Ni Y H, et al. Stochastic averaging approach to leader-following consensus of linear multi-agent systems. J Franklin I, 2016, 353: 2650–2669

    Article  MATH  MathSciNet  Google Scholar 

  103. Ni W, Wang X L, Xiong C. Leader-following consensus of multiple linear systems under switching topologies: an averaging method. Kybernetika, 2012, 48: 1194–1210

    MATH  MathSciNet  Google Scholar 

  104. Ni W, Wang X L, Xiong C. Consensus controllability, observability and robust design for leader-following linear multi-agent systems. Automatica, 2013, 49: 2199–2205

    Article  MATH  MathSciNet  Google Scholar 

  105. Chen F T, Yu H, Xia X H. Output consensus of multi-agent systems with delayed and sampled-data. IET Control Theory A, 2017, 11: 632–639

    Article  MathSciNet  Google Scholar 

  106. Cui W X, Tang Y, Fang J A, et al. Consensus analysis of second-order multi-agent networks with sampled data and packet losses. IEEE Access, 2016, 4: 8127–8137

    Article  Google Scholar 

  107. Ding L, Han Q-L, Guo G. Network-based leader-following consensus for distributed multi-agent systems. Automatica, 2013, 49: 2281–2286

    Article  MATH  MathSciNet  Google Scholar 

  108. Guo G, Ding L, Han Q L. A distributed event-triggered transmission strategy for sampled-data consensus of multiagent systems. Automatica, 2014, 50: 1489–1496

    Article  MATH  MathSciNet  Google Scholar 

  109. He W L, Zhang B, Han Q-L, et al. Leader-following consensus of nonlinear multi-agent systems with stochastic sampling. IEEE Trans Cybern, 2017, 47: 327–338

    Google Scholar 

  110. He W L, Chen G R, Han Q-L, et al. Network-based leader-following consensus of nonlinear multi-agent systems via distributed impulsive control. Inform Sci, 2017, 380: 145–158

    Article  Google Scholar 

  111. Katayama H. Design of consensus controllers for multi-rate sampled-data strict-feedback multi-agent systems. IFAC papers online, 2015, 48: 157–163

    Article  Google Scholar 

  112. Liu K X, Zhu H H, Lu J H. Bridging the gap between transmission noise and sampled data for robust consensus of multi-agent systems. IEEE Trans Circuits-I, 2015, 62: 1836–1844

    Article  MathSciNet  Google Scholar 

  113. Shen B, Wang Z D, Liu X H. Sampled-data synchronization control of complex dynamical networks with stochastic sampling. IEEE Trans Automat Contr, 2012, 57: 2644–2650

    Article  MATH  Google Scholar 

  114. Wu Y J, Wang L. Sampled-data consensus for multi-agent systems with quantised communication. Int J Control, 2015, 88: 413–428

    Article  MATH  MathSciNet  Google Scholar 

  115. Xie T T, Liao X F, Li H Q. Leader-following consensus in second-order multi-agent systems with input time delay: an event-triggered sampling approach. Neurocomputing, 2016, 177: 130–135

    Article  Google Scholar 

  116. Fan Y, Yang Y, Zhang Y. Sampling-based event-triggered consensus for multi-agent systems. Neurocomputing, 2016, 191: 141–147

    Article  Google Scholar 

  117. Zhao Y D, Zhang W D. Guaranteed cost consensus protocol design for linear multi-agent systems with sampled-data information: an input delay approach. ISA Trans, 2017, 67: 87–97

    Article  Google Scholar 

  118. Zhang X Y, Zhang J. Sampled-data consensus of general linear multi-agent systems under switching topologies: averaging method. Int J Control, 2017, 90: 291–304

    MATH  MathSciNet  Google Scholar 

  119. Wan Y, Wen G H, Cao J D, et al. Distributed node-to-node consensus of multi-agent systems with stochastic sampling. Int J Robust Nonlin, 2016, 26: 110–124

    Article  MATH  MathSciNet  Google Scholar 

  120. Wei G L, Wang L C, Liu Y R. H ∞ control for a class of multi-agent systems via a stochastic sampled-data method. IET Control Theory A, 2015, 9: 2057–2065

    Article  MathSciNet  Google Scholar 

  121. Hu A H, Cao J D, Hu M F, et al. Event-triggered consensus of Markovian jumping multi-agent systmes with stochastic sampling. IET Control Theory A, 2015, 9: 1964–1972

    Article  Google Scholar 

  122. Shang Y L. Couple-group consensus of continuous-time multi-agent systems under Markovian switching topologies. J Franklin I, 2015, 352: 4826–4844

    Article  MathSciNet  Google Scholar 

  123. Zhao H, Xu S, Yuan D. Consensus of data-sampled multi-agent systems with Markovian switching topologies. Asian J Control, 2012, 14: 1366–1373

    Article  MATH  MathSciNet  Google Scholar 

  124. Mo L, Pan T. Mean-square consensus of heterogeneous multi-agent systems under Markov switching topologies (in Chinese). Sci Sin Inform, 2016, 46: 1621–1632

    Google Scholar 

  125. Miao G Y, Li T. Mean square containment control problems of multi-agent systems under Markov switching topologies. Adv Differ Equ, 2015: 157

    Google Scholar 

  126. Miao G Y, Xu S Y, Zhang B Y, et al. Mean square consensus of second-order multi-agent systems under Markov switching topologies. IMA J Math Control I, 2014, 31: 151–164

    Article  MATH  MathSciNet  Google Scholar 

  127. Pei Y Q, Sun J T. Consensus of discrete-time linear multi-agent systems with Markov switching topologies and time-delay. Neurocomputing, 2015, 151: 776–781

    Article  Google Scholar 

  128. Ming P, Liu J C, Tan S B, et al. Consensus stabilization of stochastic multi-agent system with Markovian switching topologies and stochastic communication noise. J Franklin I, 2015, 352: 3684–3700

    Article  MathSciNet  Google Scholar 

  129. Ding L, Guo G. Sampled-data leader-following consensus for nonlinear multi-agent systems with Markovian switching topologies and communication delay. J Franklin I, 2015, 352: 369–383

    Article  MATH  MathSciNet  Google Scholar 

  130. Won K, Xiong R, Wu J. Multi-agent consensus control under Markovian switching topology and time-delay. Appl Mech Mater, 2013, 427–429: 750–4

    Google Scholar 

  131. Zhang Q, Zhang J F. Distributed consensus of continuous-time multi-agent systems with Markovian switching topologies and stochastic communication noises. J Syst Sci Math Sci, 2011, 31: 1097–1110

    MATH  MathSciNet  Google Scholar 

  132. Zhao H, Xu S, Yuan D, et al. Minimum communication cost consensus in multi-agent systems with Markov chain patterns. IET Control Theory A, 2011, 5: 63–68

    Article  MathSciNet  Google Scholar 

  133. Chen J H, Xie D M, Yu M. Consensus problem of networked multi-agent systems with constant communication delay: stochastic switching topology case. Int J Control, 2012, 85: 1248–1262

    Article  MATH  MathSciNet  Google Scholar 

  134. Liu Q Y, Wang Z D, He X, et al. A resilient approach to distributed filter design for time-varying systems under stochastic nonlinearities and sensor degradation. IEEE Trans Signal Process, 2017, 65: 1300–1309

    Article  MathSciNet  Google Scholar 

  135. Liu Y, Wang Z D, He X, et al. H ∞ filtering for nonlinear systems with stochastic sensor saturations and Markov time-delays: the asymptotic stability in probability. IET Control Theory A, 2016, 10: 1706–1715

    Article  Google Scholar 

  136. Cai C X, Wang Z D, Xu J, et al. An integrated approach to global synchronization and state estimation for nonlinear singularly perturbed complex networks. IEEE Trans Cybern, 2015, 45: 1597–1609

    Article  Google Scholar 

  137. Dong H L, Wang Z D, Ding S X, et al. Event-based H ∞ filter design for a class of nonlinear time-varying systems with fading channels and multiplicative noises. IEEE Trans Signal Process, 2015, 63: 3387–3395

    Article  MathSciNet  Google Scholar 

  138. Dong H L, Wang Z D, Ding S X, et al. Finite-horizon reliable control with randomly occurring uncertainties and nonlinearities subject to output quantization. Automatica, 2015, 52: 355–362

    Article  MATH  MathSciNet  Google Scholar 

  139. Ma L F, Wang Z D, Bo Y M, et al. A game theory approach to mixed H 2/H ∞ control for a class of stochastic time-varying systems with randomly occurring nonlinearities. Syst Control Lett, 2011, 60: 1009–1015

    Article  MATH  MathSciNet  Google Scholar 

  140. Ma L F, Wang Z D, Bo Y M, et al. Robust H ∞ sliding mode control for nonlinear stochastic systems with multiple data packet losses. Int J Robust Nonlin, 2012, 22: 473–491

    Article  MATH  MathSciNet  Google Scholar 

  141. Ma L F, Wang Z D, Han Q-L, et al. Variance-constrained distributed filtering for time-varying systems with multi-plicative noises and deception attacks over sensor networks. IEEE Sens J, 2017, 17: 2279–2288

    Article  Google Scholar 

  142. Zhang J, Ma L F, Liu Y R. Passivity analysis for discrete-time neural networks with mixed time-delays and randomly occurring quantization effects. Neurocomputing, 2016, 216: 657–665

    Article  Google Scholar 

  143. Zhang Y, Wang Z D, Ma L F. Variance-constrained state estimation for networked multi-rate systems with measurement quantization and probabilistic sensor failures. Int J Robust Nonlin, 2016, 26: 3639–3670

    MATH  MathSciNet  Google Scholar 

  144. Ma L F, Wang Z D, Lam H K, et al. Robust filtering for a class of nonlinear stochastic systems with probability constraints. Automat Rem Contr, 2016, 77: 37–54

    Article  MATH  MathSciNet  Google Scholar 

  145. Liu Y, Wang Z D, He X, et al. Finite-horizon quantized H ∞ filter design for a class of time-varying systems under event-triggered transmissions. Syst Control Lett, 2017, 103: 38–44

    Article  MATH  MathSciNet  Google Scholar 

  146. Wang L C, Wang Z D, Huang T W, et al. An event-triggered approach to state estimation for a class of complex networks with mixed time delays and nonlinearities. IEEE Trans Cybern, 2016, 46: 2497–2508

    Article  Google Scholar 

  147. Dong H L, Wang Z D, Shen B, et al. Variance-constrained H ∞ control for a class of nonlinear stochastic discrete time-varying systems: the event-triggered design. Automatica, 2016, 72: 28–36

    Article  MATH  MathSciNet  Google Scholar 

  148. Liu Q Y, Wang Z D, He X, et al. Event-based H ∞ consensus control of multi-agent systems with relative output feedback: the finite-horizon case. IEEE Trans Automat Contr, 2015, 60: 2553–2558

    Article  MATH  MathSciNet  Google Scholar 

  149. Zhang W B, Wang Z D, Liu Y R, et al. Event-based state estimation for a class of complex networks with time-varying delays: a comparison principle approach. Phys Lett A, 2017, 381: 10–18

    Article  MathSciNet  Google Scholar 

  150. Ge X H, Yang F W, Han Q L. Distributed networked control systems: a brief overview. Inform Sci, 2017, 380: 117–131

    Article  Google Scholar 

  151. Zhang X M, Han Q L. A decentralized event-triggered dissipative control scheme for systems with multiple sensors to sample the system outputs. IEEE Trans Cybern, 2016, 46: 2745–2757

    Article  Google Scholar 

  152. Zhang X M, Han Q L, Yu X. Survey on recent advances in networked control systems. IEEE Trans Ind Inform, 2016, 12: 1740–1752

    Article  Google Scholar 

  153. Zhang X M, Han Q L, 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, 13: 4–16

    Article  Google Scholar 

  154. Zou L, Wang Z D, Gao H J, et al. State estimation for discrete-time dynamical networks with time-varying delays and stochastic disturbances under the Round-Robin protocol. IEEE Trans Neural Netw, 2017, 28: 1139–1151

    Article  Google Scholar 

  155. Zou L, Wang Z D, Gao H J. Set-membership filtering for time-varying systems with mixed time-delays under Round-Robin and Weighted Try-Once-Discard protocols. Automatica, 2016, 74: 341–348

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported in part by Fundamental Research Funds for the Central Universities (Grant No. 30916011337), Postdoctoral Science Foundation of China (Grant No. 2014M551598), Research Fund for the Taishan Scholar Project of Shandong Province of China, Australian Research Council Discovery Project (Grant No. DP160103567), National Natural Science Foundation of China (Grant No. 61773209), Royal Society of the U.K., and Alexander von Humboldt Foundation of Germany.

Author information

Authors and Affiliations

  1. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, China

    Lifeng Ma

  2. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, China

    Zidong Wang

  3. Department of Computer Science, Brunel University London, Uxbridge, UB8 3PH, UK

    Zidong Wang

  4. School of Software and Electrical Engineering, Swinburne University of Technology, Melbourne, VIC, 3122, Australia

    Qing-Long Han

  5. Department of Mathematics, Yangzhou University, Yangzhou, 225002, China

    Yurong Liu

Authors
  1. Lifeng Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zidong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qing-Long Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yurong Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zidong Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ma, L., Wang, Z., Han, QL. et al. Consensus control of stochastic multi-agent systems: a survey. Sci. China Inf. Sci. 60, 120201 (2017). https://doi.org/10.1007/s11432-017-9169-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-017-9169-4

Keywords

Search

Navigation