Skip to main content
SpringerLink
Log in

Cooperative control of discrete-time linear multi-agent systems with fixed information structure

  • Brief Papers
  • Published:
Journal of Control Theory and Applications Aims and scope Submit manuscript

Abstract

In this paper, a cooperative control problem was investigated for discrete-time linear multi-agent systems with fixed information structure and without communication delays. Based on the bilinear matrix inequality (BMI), the sufficient condition was obtained for the stabilization of multi-agent systems composed of N agents. Then, the design problems of cooperative controllers were converted into the optimization problems with BMI constraints. To solve these problems, an optimization algorithm was proposed. Finally, numerical examples were provided to demonstrate the reduced conservatism of the proposed condition.

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. H. Wang. Multi-agent co-ordination for the secondary voltage control in power-system contingencies. IEE Proceedings Generation, Transmission and Distribution, 2001, 148(1): 61–66.

    Article  Google Scholar 

  2. J. Lagorse, D. Paire, A. Miraoui. A multi-agent system for energy management of distributed power sources. Renewable Energy, 2010, 35(1): 174–182.

    Article  Google Scholar 

  3. X. Zhao, S. Yuan, H. Zhou, et al. An evaluation on the multi-agent system based structural health monitoring for large scale structures. Expert System with Application, 2009, 36(3): 4900–4914.

    Article  Google Scholar 

  4. Y. Jiang, J. Jiang, T. Ishida. Compatibility between the local and social performances of multi-agent societies. Expert Systems with Applications, 2009, 36(3): 4443–4450.

    Article  Google Scholar 

  5. R. Weiskircher, N. Kontoleon, R. G. Flores, et al. Using agents for solving a multi-commodity-flow problem. European Journal of Operational Research, 2009, 194(3): 888–900.

    Article  MATH  Google Scholar 

  6. S. Sharma, H. Singh, A. Prakash. Multi-agent modeling and simulation of human behavior in aircraft evacuations. IEEE Transactions on Aerospace and Electronic Systems, 2008, 44(4): 1477–1488.

    Article  Google Scholar 

  7. M. M. H. Sarker, M. O. Tokhi. A multi-agent system model of a diesel engine using rule induction. Expert Systems with Applications, 2009, 36(3): 6044–6049.

    Article  Google Scholar 

  8. M. S. Mahmoud, M. F. Hassan, M. G. Darwish, et al. Large-scale Control Systems: Theories and Techniques. London: Wiley, 1985.

    MATH  Google Scholar 

  9. Z. Shi, W. Gao. Stabilization by decentralized control for large scale interconnected systems. Journal of Large Scale Systems, 1986, 10(2): 147–155.

    MathSciNet  MATH  Google Scholar 

  10. G. Yang, S. Zhang. Decentralized control of a class of largescale systems with symmetrically interconnected subsystems. IEEE Transactions on Automatic Control, 1996, 41(5): 710–713.

    Article  MATH  Google Scholar 

  11. X. Nian, L. Cao. BMI approach to the interconnected stability and cooperative control of Linear systems. Acta Automatica Sinica, 2008, 34(4): 438–444 (in Chinese).

    Article  MathSciNet  MATH  Google Scholar 

  12. S. Boyd, L. E. Ghaoui, E. Feron, et al. Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM, 1994.

    Book  MATH  Google Scholar 

  13. P. Gahinet, A. Nemirovski, A. Laub, et al. The LMI Control Toolbox. Natick, MA: The math Works, 1994.

    Google Scholar 

  14. K. C. Goh, M. G. Safonov, G. P. Papavassilopoulos. Global optimization for the biaffine matrix inequality problem. Journal of Global Optimization, 1995, 7(4): 365–380.

    Article  MathSciNet  MATH  Google Scholar 

  15. H. D. Tuan, P. Apkarian. Low nonconvexity-rank bilinear matrix inequalities: algorithms and applications in robust controller and structure designs. IEEE Transactions on Automatic Control, 2000, 45(11): 2111–2117.

    Article  MathSciNet  MATH  Google Scholar 

  16. F. Zheng, Q. Wang, T. H. Lee. A heuristic approach to solving a class of bilinear matrix inequality problems. Systems & Control Letters, 2002, 47(2): 111–119.

    Article  MathSciNet  MATH  Google Scholar 

  17. X. Nian. Suboptimal strategics of linear quadratic closed-loop differential games: a BMI approach. Acta Automatic Sinica, 2005, 31(2): 216–222 (in Chinese).

    MathSciNet  Google Scholar 

  18. X. Nian, X. Li, Y. Yang, et al. Bilinear matrix inequality approach to the absolute stability of interconnected Lurie control systems. Control Theory & Applications, 2005, 22(6): 999–1004 (in Chinese).

    MATH  Google Scholar 

  19. S. Wang. An example in decentralized control systems. IEEE Transactions on Automatic Control, 1978, 23(5): 938–939.

    Article  Google Scholar 

  20. D. D. Siljak. Decentralized Control of Complex Systems. New York: Academic Press, 1991.

    Google Scholar 

  21. Z. Duan, J. Wang, L. Huang. Special decentralized control problems and effectiveness of parameter-dependent Lyapunov function method. Proceedings of American Control Conference. Portland: IEEE, 2005: 1697–1702.

    Chapter  Google Scholar 

  22. Z. Duan, L. Huang, L. Wang, et al. Some applications of small gain theorem to interconnected systems. Systems & Control Letters, 2004, 52(3/4): 263–273.

    Article  MathSciNet  MATH  Google Scholar 

  23. L. Xie, L. Lu, D. Zhang, et al. Improved robust H2 and H∞ filtering for uncertain discrete-time systems. Automatica, 2004, 40(5): 873–880.

    Article  MathSciNet  MATH  Google Scholar 

  24. M. C. de Oliveira, J. Bernussou, J. C. Geromel. A new discrete-time robust stability condition. Systems & Control Letters, 1999, 37(4): 261–265.

    Article  MathSciNet  MATH  Google Scholar 

  25. M. C. de Oliveira, J. Bernussou, J. C. Geromel. Extended H2 and H∞ norm characterizations and controller parameterizations for discretetime systems. International Journal of Control, 2002, 75(9): 371–381.

    Google Scholar 

  26. S. Berard, J. Trinkle, B. Nguyen, et al. daVinci code: A multi-model simulation and analysis tool for multi-body systems. 2007 IEEE International Conference on Robotics and Automation. Roma: IEEE, 2007: 2588–2593.

    Chapter  Google Scholar 

  27. Z. Li, Z. Duan, L. Huang. H∞ control of networked multi-agent systems. Journal of Systems Science and Complexity, 2009, 22(1): 35–48.

    Article  MathSciNet  MATH  Google Scholar 

  28. Z. Li, Z. Duan, G. Chen, et al. Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint. IEEE Transactions on Circuits and Systems I: Regular Paper, 2010, 57(1): 213–224.

    Article  MathSciNet  Google Scholar 

  29. Z. Duan, J. Wang, L. Huang. Special decentralized control problems in discrete-time interconnected systems composed of two subsystems. Systems Control Letters, 2007, 56(3): 206–214.

    Article  MathSciNet  MATH  Google Scholar 

  30. R. A. Horn, C. R. Johnson. Topics in Matrix Analysis. New York: Cambridge University Press, 1994.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha Hunan, 410083, China

    Jing Wang, Xiaohong Nian & Haibo Wang

Authors
  1. Jing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaohong Nian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haibo Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaohong Nian.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 61075065, 60774045, U1134108), and the Ph.D. Programs Foundation of Ministry of Education of China (No. 20110162110041).

Jing WANG was born in Kaifeng, Henan, China, in 1985. She received her B.S. degree in Automation from Changsha University of Science and Technology in 2007. She is a M.S. candidate at Central South University. Her research interests include theory of cooperative control and consensus problem of discrete-time multi-agent systems.

Xiaohong NIAN was born in Tianshui, Gansu, China, in 1965. He received his B.S., M.S., and Ph.D. degrees from Northwest Normal University, Shandong University and Peking University, in 1985, 1992 and 2004, respectively. Currently, he is a professor at Central South University. His research interests include robust control, theory of differential games, and induction motor control.

Haibo WANG received his B.S., M.S., and Ph.D. degrees from Bohai University, Northeastern University and The University of Hong Kong, in 1992, 1998 and 2002, respectively. From 2002 to 2005, he was postdoctoral researcher in Nanyang Technological University. Currently, he is a professor at Central South University. His research interests include fault detection, faulttolerant control and intelligent control.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, J., Nian, X. & Wang, H. Cooperative control of discrete-time linear multi-agent systems with fixed information structure. J. Control Theory Appl. 10, 403–409 (2012). https://doi.org/10.1007/s11768-012-0082-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-012-0082-2

Keywords

Search

Navigation