Skip to main content

Distributed Impulsive Control of Leader-Following Multi-agent Systems

  • Living reference work entry
  • First Online:
Handbook of Real-Time Computing
  • 30 Accesses

Abstract

This chapter focuses on leader-follower consensus of nonlinear multi-agent systems in homogenous networks and heterogenous networks via distributed impulsive control, respectively. Leader-follower consensus problem in homogenous networks is studied in Sect. 2. Then in Sect. 3, a network-based leader-following consensus problem is considered, and distributed delayed impulsive protocols are designed for nonlinear multi-agent systems. Finally, bounded leader-follower consensus problem is well investigated in heterogenous networks in Sect. 4. How to obtain a tight error bound, to optimize the error bound, and to design the impulse intervals and coupling strength within a prescribed error bound are addressed.

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

Access this chapter

Institutional subscriptions

Similar content being viewed by others

References

  • R. Bhatia, Matrix Analysis (Springer, New York, 1997)

    Book  Google Scholar 

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

    Article  Google Scholar 

  • W. Chen, W. Zheng, Exponential stability of nonlinear time-delay system with delayed impulse effects. Automatica 47(5), 1075–1083 (2011)

    Article  MathSciNet  Google Scholar 

  • T. Chen, X. Liu, W. Lu, Pinning complex networks by a single controller. IEEE Trans. Circuits Syst. I: Reg. Pap. 54(6), 1317–1326 (2007)

    Article  MathSciNet  Google Scholar 

  • Y. Chen, W. Yu, F. Li, S. Feng, Synchronization of complex networks with impulsive control and disconnected topology. IEEE Trans. Circuits Syst. II: Express Briefs 60(5), 292–296 (2013a)

    Article  Google Scholar 

  • W. Chen, D. Wei, W. Zheng, Delayed impulsive control of Takagi–Sugeno fuzzy delay systems. IEEE Trans. Fuzzy Syst. 21(3), 516–526 (2013b)

    Article  Google Scholar 

  • L. Ding, P. Yu, Z. Liu, Z. Guan, G. Feng, Consensus of second-order multi-agent systems via impulsive control using sampled hetero-information. Automatica 49(9), 2881–2886 (2013)

    Article  MathSciNet  Google Scholar 

  • Z. Guan, Z. Liu, G. Feng, Y. Wang, Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control. IEEE Trans. Circuits Syst. I: Reg. Pap. 57(8), 2182–2195 (2010)

    Article  MathSciNet  Google Scholar 

  • Z. Guan, Z.W. Liu, G. Feng, M. Jian, Impulsive consensus algorithms for second-order multi-agent networks with sampled information. Automatica 48(7), 1397–1404 (2012)

    Article  MathSciNet  Google Scholar 

  • G. Guo, Linear systems with medium-access constraint and Markov actuator assignment. IEEE Trans. Circuits Syst. I: Reg. Pap. 57(11), 2999–3010 (2010)

    Article  MathSciNet  Google Scholar 

  • G. Guo, Z. Lu, Q.-L. Han, Control with Markov sensors/actuators assignment. IEEE Trans. Autom. Control 57(7), 1799–1804 (2012)

    Article  MathSciNet  Google Scholar 

  • W. He, F. Qian, J. Lam, G. Chen, Q.-L. Han, J. Kurths, Quasi-synchronization of heterogenous dynamic networks via distributed impulsive control: error estimation, optimization and design. Automatica 62, 249–262 (2015)

    Article  Google Scholar 

  • W. He, G. Chen, Q.-L. Han, F. Qian, Impulsive consensus for complex dynamical networks with nonidentical nodes and coupling time-delays. Inf. Sci. 380, 145–158 (2017)

    Article  Google Scholar 

  • T. Huang, C. Li, X. Liao, Synchronization of a class of coupled chaotic delayed systems with parameter mismatch. Chaos 17(3), 033121 (2007)

    Google Scholar 

  • H. Hu, A. Liu, Q. Xuan, L. Yu, G. Xie, Second-order consensus of multi-agent systems in the cooperation–competition network with switching topologies: a time-delayed impulsive control approach. Syst. Control Lett. 62(12), 1125–1135 (2013)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • X. Jiang, Q.-L. Han, S. Liu, A. Xue, A new stabilization criterion for networked control systems. IEEE Trans. Autom. Control 53(4), 1025–1032 (2008)

    Article  MathSciNet  Google Scholar 

  • A. Khadra, X. Liu, X. Shen, Analyzing the robustness of impulsive synchronization coupled by linear delayed impulses. IEEE Trans. Autom. Control 54(4), 923–928 (2009)

    Article  MathSciNet  Google Scholar 

  • F. Lian, W. Moyne, D. Tilbury, Network design consideration for distributed control systems. IEEE Trans. Control Syst. Technol. 10(2), 297–307 (2002)

    Article  Google Scholar 

  • H. Li, X. Liao, T. Huang, Y. Wang, Q.-L. Han, T. Dong, Algebraic criteria for second-order global consensus in multi-agent networks with intrinsic nonlinear dynamics and directed topologies. Inf. Sci. 259, 25–35 (2014)

    Article  MathSciNet  Google Scholar 

  • B. Liu, D. Hill, Impulsive consensus for complex dynamical networks with nonidentical nodes and coupling time-delays. SIAM J. Control Optim. 49(2), 315–338 (2011)

    Article  MathSciNet  Google Scholar 

  • B. Liu, X. Liu, G. Chen, H. Wang, Robust impulsive synchronization of uncertain dynamical networks. IEEE Trans. Circuits Syst. I: Reg. Pap. 52(7), 1431–1441 (2005)

    Article  MathSciNet  Google Scholar 

  • W. Lu, X. Li, Z. Rong, Global stabilization of complex networks with digraph topologies via a local pinning algorithm. Automatica 46(1), 116–121 (2010a)

    Article  MathSciNet  Google Scholar 

  • J. Lu, D.W.C. Ho, J. Cao, A unified synchronization criterion for impulsive dynamical networks. Automatica 46(7), 1215–1221 (2010b)

    Article  MathSciNet  Google Scholar 

  • J. Lu, J. Kurths, J. Cao, N. Mahdavi, C. Huang, Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy. IEEE Trans. Neural Netw. Learn. Syst. 23(2), 285–292 (2012)

    Article  Google Scholar 

  • C. Peng, Q.-L. Han, A novel event-triggered transmission scheme and l2 control co-design for sampled-data control systems. IEEE Trans. Autom. Control 58(10), 2620–2626 (2013)

    Article  Google Scholar 

  • C. Peng, Q.-L. Han, D. Yue, To transmit or not to transmit: a discrete event-triggered communication scheme for networked takagi-sugeno fuzzy systems, IEEE Trans. Fuzzy Syst. 21(1), 164–170 (2013)

    Article  Google Scholar 

  • Q. Song, F. Liu, J. Cao, W. Yu, M-matrix strategies for pinning-controlled leader-following consensus in multiagent systems with nonlinear dynamics. IEEE Trans. Cybern. 43(6), 1688–1697 (2013)

    Article  Google Scholar 

  • F. Sorrentino, M. Di Bernardo, F. Garofalo, G. Chen, Controllability of complex networks via pinning. Phys. Rev. E 75(4), 046103 (2007)

    Google Scholar 

  • H. Su, M.Z.Q. Chen, J. Lam, Z. Lin, Semi-global leader-following consensus of linear multi-agent systems with input saturation via low gain feedback. IEEE Trans. Circuits Syst. I: Reg. Pap. 60(7), 1881–1889 (2013)

    Article  MathSciNet  Google Scholar 

  • Y. Tang, Z. Wang, J. Fang, Controller design for synchronization of an array of delayed neural networks using a controllable probabilistic pso, Inf. Sci. 181, 4715–4732 (2011)

    Article  Google Scholar 

  • T. Yang, Impulsive Control Theory (Springer, Berlin, 2001)

    MATH  Google Scholar 

  • Z. Yang, D. Xu, Stability analysis and design of impulsive control systems with time delay. IEEE Trans. Autom. Control 52(8), 1448–1454 (2007)

    Article  MathSciNet  Google Scholar 

  • W. Yu, G. Chen, J. Lü, On pinning synchronization of complex dynamical networks. Automatica 45(2), 429–435 (2009)

    Article  MathSciNet  Google Scholar 

  • H. Zhang, J. Zhou, Distributed impulsive consensus for second-order multi-agent systems with input delays. IET Control Theory Appl. 7(16), 1978–1983 (2013)

    Article  MathSciNet  Google Scholar 

  • W. Zhang, Y. Tang, Q. Miao, J. Fang, Synchronization of stochastic dynamical networks under impulsive control with time delays. IEEE Trans. Neural Netw. Learn. Syst. 25(10), 1758–1768 (2014a)

    Article  Google Scholar 

  • W. Zhang, Y. Tang, X. Wu, J. Fang, Synchronization of nonlinear dynamical networks with heterogeneous impulses. IEEE Trans. Circuits Syst. I: Reg. Pap. 61(4), 1220–1228 (2014b)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wangli He .

Editor information

Editors and Affiliations

Section Editor information

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

He, W., Qian, F., Chen, G., Han, QL. (2019). Distributed Impulsive Control of Leader-Following Multi-agent Systems. In: Tian, YC., Levy, D.C. (eds) Handbook of Real-Time Computing. Springer, Singapore. https://doi.org/10.1007/978-981-4585-87-3_17-1

Download citation

  • DOI: https://doi.org/10.1007/978-981-4585-87-3_17-1

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-4585-87-3

  • Online ISBN: 978-981-4585-87-3

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics