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Distributed algorithm for dissensus of a class of networked multiagent systems using output information

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Abstract

In this paper, a distributed algorithm is developed to solve the dissensus of a class of networked multiagent systems only using output information. By introducing a gauge transformation, the dissensus problem is transformed to the problem of demonstrating that (A, B, C) is stabilizable and detectable. If the networked multiagent systems can reach dissensus, the signed digraph is structurally balanced containing a spanning tree. Furthermore, by solving a Riccati equation, the necessary condition becomes a necessary and sufficient condition. Finally, two examples are provided to illustrate our results. There are three main contributions in this paper: (1) a distributed algorithm with output information is introduced to deal with the difficulty of obtaining relative full-state observations; (2) the undirected communication graph is extended to the signed digraph which is more practical in physical implementations; (3) the method established in this paper is also applicable to discrete-time networked multiagent systems by using a gauge transformation, which further demonstrates the generality of our results.

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References

  • Altafini C (2013) Consensus problems on networks with antagonistic interactions. IEEE Trans Autom Control 58(4):935–946

    Article  MathSciNet  MATH  Google Scholar 

  • Bertsekas DP, Tsitsiklis JN (1989) Parallel and distributed computation: numerical methods. Printice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Cao Y, Yu W, Ren W, Chen G (2013) An overview of recent progress in the study of distributed multi-agent coordination. IEEE Trans Ind Inf 9(1):427–438

    Article  Google Scholar 

  • Cheng L, Hou ZG, Tan M, Lin Y, Zhang W (2010) Neural-network-based adaptive leader-following control for multiagent systems with uncertainties. IEEE Trans Neural Netw 21(8):1351–1358

    Article  Google Scholar 

  • Cheng L, Hou ZG, Tan M (2014) A mean square consensus protocol for linear multi-agent systems with communication noises and fixed topologies. IEEE Trans Autom Control 59(1):261–267

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng Z, Ma S (2006) Linear system theory. Science Press, Beijing

    Google Scholar 

  • Diestel R (2000) Graph theory. Springer, New York

    MATH  Google Scholar 

  • He W, Ge SS (2016) Cooperative control of a nonuniform gantry crane with constrained tension. Automatica 66(4):146–154

    Article  MathSciNet  MATH  Google Scholar 

  • Hu JP, Zheng WX (2013) Bipartite consensus for multi-agent systems on directed signed networks. In: Proceedings of the IEEE conference on decision and control. Florence, Italy, pp 3451–3456

  • Hu JP, Xiao ZH, Zhou YL, Yu JY (2013) Formation control over antagonistic networks. In: Proceedings of the Chinese control conference. Xi’an, China, pp 6879–6884

  • Jadbabaie A, Lin J, Morse AS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control 48(6):988–1001

    Article  MathSciNet  MATH  Google Scholar 

  • Liang H, Zhang H, Wang Z, Wang J (2014) Consensus robust output regulation of discrete-time linear multi-agent systems. IEEE/CAA J Autom Sinica 1(2):204–209

    Article  Google Scholar 

  • Lin P, Ren W (2014) Constrained consensus in unbalanced networks with communication delays. IEEE Trans Autom Control 59(3):775–781

    Article  MathSciNet  MATH  Google Scholar 

  • Liu C, Kroll A (2015) Memetic algorithms for optimal task allocation in multi-robot systems for inspection problems with cooperative tasks. Soft Comput 19(3):567–584

    Article  Google Scholar 

  • Liu D, Wang D, Li H (2014) Decentralized stabilization for a class of continuous-time nonlinear interconnected systems using online learning optimal control approach. IEEE Trans Neural Netw Learn Syst 25(2):418–428

    Article  Google Scholar 

  • Liu T, Jiang ZP (2013) Distributed formation control of nonholonomic mobile robots without global position measurements. Automatica 49(2):592–600

    Article  MathSciNet  MATH  Google Scholar 

  • Liu T, Jiang ZP (2014) Distributed control of nonlinear uncertain systems: a cyclic-small-gain approach. IEEE/CAA J Autom Sinica 1(1):46–53

    Article  Google Scholar 

  • Luo X, Feng L, Yan J, Guan X (2015) Dynamic coverage with wireless sensor and actor networks in underwater environment. IEEE/CAA J Autom Sinica 2(3):274–281

    Article  MathSciNet  Google Scholar 

  • Ma C (2009) System analysis and control synthesis of linear multi-agent systems. PhD thesis, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, China

  • Ma CQ, Zhang JF (2010) Necessary and sufficient conditions for consensusability of linear multi-agent systems. IEEE Trans Autom Control 55(5):1263–1268

    Article  MathSciNet  MATH  Google Scholar 

  • Ma H, Liu D, Wang D (2015a) Distributed control for nonlinear time-delayed multi-agent systems with connectivity preservation using neural networks. In: Proceedings of the 22nd international conference on neural information processing. Istanbul, Turkey, pp 34–42

  • Ma H, Liu D, Wang D, Tan F, Li C (2015b) Centralized and decentralized event-triggered control for group consensus with fixed topology in continuous time. Neurocomputing 161:267–276

    Article  Google Scholar 

  • Ma H, Liu D, Wang D, Luo B (2016a) Bipartite output consensus in networked multi-agent systems of high-order power integrators with signed digraph and input noises. Int J Syst Sci 47(13):3116–3131

    Article  MathSciNet  MATH  Google Scholar 

  • Ma H, Wang Z, Wang D, Liu D, Yan P, Wei Q (2016b) Neural-network-based distributed adaptive robust control for a class of nonlinear multiagent systems with time delays and external noises. IEEE Trans Syst Man Cybern Syst 46(6):750–758

  • Olfati-Saber R, Fax JA, Murray RM (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95(1):215–233

    Article  MATH  Google Scholar 

  • Quteishat A, Lim CP, Saleh JM, Tweedale J, Jain LC (2011) A neural network-based multi-agent classifier system with a bayesian formalism for trust measurement. Soft Comput 15(2):221–231

    Article  Google Scholar 

  • Ren W, Beard RW (2005) Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Autom Control 50(5):655–661

    Article  MathSciNet  MATH  Google Scholar 

  • Scheepers C, Engelbrecht AP (2016) Training multi-agent teams from zero knowledge with the competitive coevolutionary team-based particle swarm optimiser. Soft Comput 20(2):607–620

    Article  Google Scholar 

  • Shen J, Tan H, Wang J, Wang J, Lee S (2015) A novel routing protocol providing good transmission reliability in underwater sensor networks. J Internet Technol 16(1):171–178

    Google Scholar 

  • Smith HL (1995) Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. American Mathematical Society, Providence

    MATH  Google Scholar 

  • Tsitsiklis JN (1984) Problems in decentralized decision making and computation. PhD thesis, Department of EECS, MIT, Cambridge, MA, USA

  • Valcher ME, Misra P (2014) On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions. Syst Control Lett 66:94–103

    Article  MathSciNet  MATH  Google Scholar 

  • Vicsek T, Czirók A, Ben-Jacob E, Cohen I, Shochet O (1995) Novel type of phase transition in a system of self-driven particles. Phys Rev Lett 75(6):1226–1229

    Article  MathSciNet  Google Scholar 

  • Wang D, Li C, Liu D, Mu C (2016a) Data-based robust optimal control of continuous-time affine nonlinear systems with matched uncertainties. Inf Sci 366:121–133

  • Wang D, Liu D, Li H, Ma H, Li C (2016b) A neural-network-based online optimal control approach for nonlinear robust decentralized stabilization. Soft Comput 20(2):707–716

    Article  MATH  Google Scholar 

  • Wang D, Ma H, Liu D (2016c) Distributed control algorithm for bipartite consensus of the nonlinear time-delayed multi-agent systems with neural networks. Neurocomputing 174:928–936

    Article  Google Scholar 

  • Wieland P, Kim JS, Allgöwer F (2011) On topology and dynamics of consensus among linear high-order agents. Int J Syst Sci 42(10):1831–1842

    Article  MathSciNet  MATH  Google Scholar 

  • Xie S, Wang Y (2014) Construction of tree network with limited delivery latency in homogeneous wireless sensor networks. Wirel Pers Commun 78(1):231–246

    Article  Google Scholar 

  • Zhang H, Qin C, Jiang B, Luo Y (2014) Online adaptive policy learning algorithm for \(h_{\infty }\) state feedback control of unknown affine nonlinear discrete-time systems. IEEE Trans Cybern 44(12):2706–2718

    Article  Google Scholar 

  • Zhang H, Feng T, Yang GH, Liang H (2015a) Distributed cooperative optimal control for multiagent systems on directed graphs: an inverse optimal approach. IEEE Trans Cybern 45(7):1315–1326

    Article  Google Scholar 

  • Zhang H, Zhang J, Yang GH, Luo Y (2015b) Leader-based optimal coordination control for the consensus problem of multi-agent differential games via fuzzy adaptive dynamic programming. IEEE Trans Fuzzy Syst 23(1):152–163

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grants 61233001, 61273140, 61304086, 61533017, 61503379 and U1501251, in part by China Scholarship Council under the State Scholarship Fund, in part by Beijing Natural Science Foundation under Grant 4162065 and in part by the Early Career Development Award of SKLMCCS.

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Authors and Affiliations

  1. The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, 100190, Beijing, China

    Hongwen Ma, Ding Wang & Hongliang Li

  2. University of Chinese Academy of Sciences, 100190, Beijing, China

    Hongwen Ma

  3. School of Automation and Electrical Engineering, University of Science and Technology Beijing, 100083, Beijing, China

    Derong Liu

  4. School of Electrical Engineering and Automation, Tianjin University, 300072, Tianjin, China

    Xiong Yang

Authors
  1. Hongwen Ma
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  2. Derong Liu
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  3. Ding Wang
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  4. Xiong Yang
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  5. Hongliang Li
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Correspondence to Derong Liu.

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The authors declare that they have no conflict of interest.

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Communicated by V. Loia.

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Ma, H., Liu, D., Wang, D. et al. Distributed algorithm for dissensus of a class of networked multiagent systems using output information. Soft Comput 22, 273–282 (2018). https://doi.org/10.1007/s00500-016-2332-6

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