Skip to main content
SpringerLink
Log in

A consensus problem for a class of vehicles with 2-D dynamics

  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, we consider the problem of a kind of consensus problem among a collection of vehicles performing a shared task with 2-D Fornasini-Marchesini second local state-space (LSS) dynamical model by using intervehicle communication and output feedback themselves in which the weights of the corresponding edges are considered as the control variables. Firstly, it is shown that under certain conditions, the stability of a collection of N identical vehicles can be equivalently transferred into the stability analysis of a single vehicle with the same dynamics, modified by only a scalar, representing the interconnection, that takes values according to the eigenvalues of the weights matrix. Then, two types of networks, star-shaped networks and globally coupled networks, are studied in details. Secondly, the general description are presented for such consensus problem via the block diagram of information flow. Finally, a collection of vehicles with different 2-D LSS dynamical model is investigated.

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

  • Bender J. G. (1991) An overview of systems studies of automated highway systems. IEEE Transactions on Vehicular Technology 40(1): 82–99

    Article  Google Scholar 

  • Boyd S. P., Ghaoui L. E., Feron E., Balakrishnan V. (1998) Linear matrix inequalities in system and control theory. SIAM, Philadelphia, PA

    Google Scholar 

  • Buzogany, L. E., Pachter, M., d’Azzo, J. J. (1993). Automated control of aircraft in formation flight. In Proceedings of the AIAA Conference Guidance, Navigation, and Control (pp. 1349–1370).

  • Chai W. W., Chua L. O. (1995) Application of Kronecker products to the analysis of systems with uniform linear coupling. IEEE Transactions on Circuits and Systems-I 42(10): 775–778

    Article  Google Scholar 

  • Chen J. L., Chen X. H. (2001) Special matrices. Tsinghua, Beijing

    Google Scholar 

  • Corts J., Martnez S., Bullo F. (2005) Spatially-distributed coverage optimization and control with limited-range interactions. ESAIM: Control, Optimisation and Calculus of Variations 11(4): 691–719

    Article  MathSciNet  Google Scholar 

  • Corts J., Martnez S., Bullo F. (2006) Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions. IEEE Transactions on Automatic Control 51(8): 1289–1298

    Article  Google Scholar 

  • de Berg M., van Kreveld M., Overmars M., Schwarzkopf O. (2000) Computational geometry: Algorithms and applications (2nd ed.). Springer-Verlag, New York

    MATH  Google Scholar 

  • Derenick J., Spletzer J., Hsieh A. (2009) An optimal approach to collaborative target tracking with performance guarantees. Journal of Intelligent and Robotic Systems 56: 47–67

    Article  Google Scholar 

  • Duan Z. S., Wang J. Z., Chen G. R., Huang L. (2008) Stability analysis and decentralized control of a class of complex dynamical networks. Automatica 44(4): 1028–1035

    MathSciNet  Google Scholar 

  • Fax J. A., Murray R. M. (2004) Information flow and cooperative control of vehicle formations. IEEE Transactions on Automatic Control 49(9): 1465–1476

    Article  MathSciNet  Google Scholar 

  • Fornasini E., Marchesini G. (1978) Doubly-indexed dynamical systems: State-space models and structural properties. Mathematical Systems Theory 12(1): 59–72

    Article  MathSciNet  MATH  Google Scholar 

  • Galkowski K., Rogers E., Xu S., Lam J., Owens D. H. (2002) LMIs-A fundamental tool in analysis and controller design for discrete linear repetitive processes. IEEE Transactions on Circuits Systems I, Fundamental Theory and Applications 49(6): 768–778

    Article  MathSciNet  Google Scholar 

  • Gumel A.B., Ruan S., Day T. et al (2004) Modeling strategies for controlling SARS outbreaks. Proceedings of the royal society 271(1554): 2223–2232

    Article  Google Scholar 

  • Hinamoto T. (1993) 2-D lyapunov equation and filter design based on the Fornasini-Marchesinni second model. IEEE Transactions on Circuits Systems I, Fundamental Theory and Applications 40(2): 102–110

    Article  MATH  Google Scholar 

  • Huang L., Duan Z. S. (2003) Complexity in control science. Acta Automatica Sinica 29(5): 748–753

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Jaromczyk J.W., Toussaint G.T. (1992) Relative neighborhood graphs and their relatives. Proceedings of the IEEE 80(9): 1502–1517

    Article  Google Scholar 

  • Martnez S., Corts J., Bullo F. (2007) Motion coordination with distributed information. IEEE Control Systems Magzine 27(1): 75–87

    Article  Google Scholar 

  • Moreau L. (2005) Stability of multiagent systems with time-dependent communication links. IEEE Transactions on Automatic Control 50(2): 169–182

    Article  MathSciNet  Google Scholar 

  • Ohara, A., & Sasaki, Y. (2001). On solvability and numerical solutions of parameter- dependent differential matrix inequality. In Proceedings of the IEEE Conference Decision Control, Orlando (pp. 3593–3594) FL.

  • Olfati-Saber R., Murray R. M. (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control 49(9): 1520–1533

    Article  MathSciNet  Google Scholar 

  • Packard A., Doyle J. C. (1993) The complex structured singular value. Automatica 29(1): 71–109

    Article  MathSciNet  MATH  Google Scholar 

  • Ren W., Beard R. W., Atkins E. M. (2007) Information consensus in multivehicle cooperative control: Collective group behavior through local interaction. IEEE Control Systems Magazine 27(2): 71–82

    Article  Google Scholar 

  • Schaub H. et al (2000) Spacecraft formation flying control using mean orbital elements. Journal of Astronautical Science 48(1): 69–87

    Google Scholar 

  • Smith, T. R., mann, H. H., & Leonard, N. E. (2001). Orientation control of multiple underwater vehicles, In Proceedings of the 40th IEEE Conference Decision and Control (pp. 4598–4603).

  • Sun K., Zheng D. Z., Lu Q. (2003) Splitting strategies for islanding operation of large-scale power systems using OBDD-based methods. IEEE Transactions on Power Systems 18(2): 912–923

    Article  Google Scholar 

  • Yamaguchi H., Arai T., Beni G. (2001) A distributed control scheme for multiple robotic vehicles to make group formations. Robotics and Autonomous systems 36(4): 125–147

    Article  Google Scholar 

  • Yan X., Zou Y. (2008) Optimal and sub-optimal quarantine and isolation control in SARS epidemics. Mathematical and Computer Modeling 47(1): 235–245

    Article  MathSciNet  MATH  Google Scholar 

  • Yan X. F., Zou Y. (2009) Isolation treatment strategy for emergency control. Journal of systems engineering 24(2): 129–135

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automation, Nanjing University of Science and Technology, 210094, Nanjing, Jiangsu, People’s Republic of China

    Xinjin Liu & Yun Zou

Authors
  1. Xinjin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yun Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yun Zou.

Additional information

This work was supported in part by the National Natural Science Foundation of P.R. China under Grant 60874007 and the Research Fund for the Doctoral Program of Higher Education 200802550024.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, X., Zou, Y. A consensus problem for a class of vehicles with 2-D dynamics. Multidim Syst Sign Process 21, 373–389 (2010). https://doi.org/10.1007/s11045-010-0121-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11045-010-0121-4

Keywords

Search

Navigation