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Output regulation of multiple heterogeneous switched linear systems

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Abstract

This paper addresses the cooperative output regulation problem of a class of multi-agent systems (MASs). Each agent is a switched linear system. We propose an agent-dependent multiple Lyapunov function (MLF) approach to design the switching law for each switched agent. The distributed controller for each agent is constructed based on a dynamic compensator. A sufficient condition for the solvability of the output regulation problem of switched agent networks is presented by distributed controllers and agent-dependent multiple Lyapunov function approach. Finally, simulation results demonstrate the effectiveness of our theory.

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References

  1. D. Liberzon. Switching in Systems and Control, Boston, USA: Birkhäuser, 2003.

    Book  MATH  Google Scholar 

  2. H. Lin, P. J. Antsaklis. Stability and stabilizability of switched linear systems: A survey of recent results. IEEE Transactions on Automatic Control, vol. 54, no. 2, pp. 308–322, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  3. C. Tomlin, G. J. Pappas, S. Sastry. Conflict resolution for air traffic management: A study in multiagent hybrid systems. IEEE Transactions on Automatic Control, vol. 43, no. 4, pp. 509–521, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  4. D. Jeon, M. Tomizuka. Learning hybrid force and position control of robot manipulators. IEEE Transactions on Automatic Control, vol. 9, no. 4, pp. 423–431, 1993.

    Article  Google Scholar 

  5. S. M. William, R. G. Hoft. Adaptive frequency domain control of PWM switched power line conditioner. IEEE Transactions on Power Electronics, vol. 6, no. 4, pp. 665–670, 1991.

    Article  Google Scholar 

  6. D. Liberzon, A. S. Morse. Basic problems in stability and design of switched systems. IEEE Control Systems, vol. 19, no. 5, pp. 57–70, 1999.

    MATH  Google Scholar 

  7. X. Q. Zhang, J. Zhao. L 2-gain Analysis and anti-windup design of discrete-time switched systems with actuator saturation. International Journal of Automation and Computing, vol. 9, no. 4, pp. 369–377, 2012.

    Article  Google Scholar 

  8. P. Peleties, R. DeCarlo. Asymptotic stability of m-switched systems using Lyapunov-like functions. In Proceedings of the American Control Conference, IEEE, Boston, USA, USA, pp. 1679–1684, 1991.

    Google Scholar 

  9. J. Lu, L. J. Brown. A multiple Lyapunov functions approach for stability of switched systems. In Proceedings of American Control Conference, IEEE, Baltimore, USA, pp. 3253–3256, 2010.

    Google Scholar 

  10. B. Niu, J. Zhao. Robust H ∞ control for a class of switched nonlinear cascade systems via multiple Lyapunov functions approach. AppliedMathematics and Computation, vol. 218, no. 11, pp. 6330–6339, 2012.

    MathSciNet  MATH  Google Scholar 

  11. J. P. Hespanha, A. S. Morse. Stability of switched systems with average dwell-time. In Proceedings of the 38th IEEE Conference on Decision and Control, IEEE, Phoenix, USA, pp. 2655–2660, 1999.

    Google Scholar 

  12. G. S. Zhai, B. Hu, K. Yasuda, A. N. Michel. Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach. International Journal of Systems Science, vol. 32, no. 8, pp. 1055–1061, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  13. W. Ren, Y. C. Cao. Distributed Coordination of Multi-Agent Networks: Emergent Problems, Models, and Issues, London, UK: Springer-Verlag, 2011.

    Book  MATH  Google Scholar 

  14. P. P. Dai, C. L. Liu, F. Liu. Consensus problem of heterogeneous multi-agent systems with time delay under fixed and switching topologies. International Journal of Automation and Computing, vol. 11, no. 3, pp. 340–346, 2014.

    Article  Google Scholar 

  15. M. I. Menhas, L. Wang, M. R. Fei, C. X. Ma. Coordinated controller tuning of a boiler turbine unit with new binary particle swarm optimization algorithm. International Journal of Automation and Computing, vol. 8, no. 2, pp. 185–192, 2011.

    Article  Google Scholar 

  16. R. Olfati-Saber. Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE Transactions on Automatic Control, vol. 51, no. 3, pp. 401–420, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  17. B. Das, B. Subudhi, B. B. Pati. Cooperative formation control of autonomous underwater vehicles: An overview. International Journal of Automation and Computing, vol. 13, no. 3, pp. 199–225, 2016.

    Article  Google Scholar 

  18. A. Isidori. Nonlinear Control Systems II, New York, USA: Springer-Verlag, 1999.

    Book  MATH  Google Scholar 

  19. J. Huang. Nonlinear Output Regulation: Theory and Applications, Philadelphia, USA: SIAM, 2004.

    Book  MATH  Google Scholar 

  20. B. A. Francis, W. M. Wonham. The internal model principle for linear multivariable regulators. AppliedMathematics and Optimization, vol. 2, no. 2, pp. 170–194, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  21. J. Huang, Z. Y. Chen. A general framework for tackling the output regulation problem. IEEE Transactions on Automatic Control, vol. 49, no. 12, pp. 2203–2218, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  22. X. X. Dong, J. Zhao. Solvability of the output regulation problem for switched non-linear systems. IET Control Theory & Applications, vol. 6, no. 8, pp. 1130–1136, 2012.

    Article  MathSciNet  Google Scholar 

  23. L. J. Long, J. Zhao. Robust and decentralised output regulation of switched non-linear systems with switched internal model. IET Control Theory & Applications, vol. 8, no. 8, pp. 561–573, 2014.

    Article  MathSciNet  Google Scholar 

  24. Y. F. Su, J. Huang. Cooperative output regulation of linear multi-agent systems. IEEE Transactions on Automatic Control, vol. 57, no. 4, pp. 1062–1066, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  25. Z. T. Ding. Consensus output regulation of a class of heterogeneous nonlinear systems. IEEE Transactions on Automatic Control, vol. 58, no. 10, pp. 2648–2653, 2013.

    Article  MathSciNet  MATH  Google Scholar 

  26. J. Xiang, W. Wei, Y. J. Li. Synchronized output regulation of linear networked systems. IEEE Transactions on Automatic Control, vol. 54, no. 6, pp. 1336–1341, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  27. D. B. Xu, Y. G. Hong, X. H. Wang. Distributed output regulation of nonlinear multi-agent systems via host internal model. IEEE Transactions on Automatic Control, vol. 59, no. 10, pp. 2784–2789, 2014.

    Article  MathSciNet  MATH  Google Scholar 

  28. Y. G. Hong, L. X. Gao, D. Z. Cheng, J. P. Hu. Lyapunovbased approach to multiagent systems with switching jointly connected interconnection. IEEE Transactions on Automatic Control, vol. 52, no. 5, pp. 943–948, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  29. W. Y. Xu, J. D. Cao, W. W. Yu, J. Q. Lu. Leader-following consensus of non-linear multi-agent systems with jointly connected topology. IET Control Theory & Applications, vol. 8, no. 6, pp. 432–440, 2014.

    Article  MathSciNet  Google Scholar 

  30. W. Y. Xu, D.W. C. Ho, L. L. Li, J. D. Cao. Event-triggered schemes on leader-following consensus of general linear multiagent systems under different topologies. IEEE Transactions on Cybernetics, to be published.

  31. H. W. Jia, J. Zhao. Output regulation of switched linear multi-agent systems: An agent-dependent average dwell time method. International Journal of Systems Science, vol. 47, no. 11, pp. 2510–2520, 2016.

    Article  MathSciNet  MATH  Google Scholar 

  32. A. Cervantes-Herrera, J. Ruiz-León, C. López-Limón, A. Ramirez-Trevino. A distributed control design for the output regulation and output consensus of a class of switched linear multi-agent systems. In Proceedings of the 17th International Conference on Emerging Technologies & Factory Automation, IEEE, Krakow, Poland, pp. 1–7, 2012.

    Google Scholar 

  33. A. S. Morse, D. Q. Mayne, G. C. Goodwin. Applications of hysteresis switching in parameter adaptive control. IEEE Transactions on Automatic Control, vol. 37, no. 9, pp. 1343–1354, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  34. J. P. Hespanha, D. Liberzon, A. S. Morse. Hysteresis-based switching algorithms for supervisory control of uncertain system. Automatica, vol. 39, no. 2, pp. 263–272, 2003.

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Nos. 61304058 and 61233002), IAPI Fundamental Research Funds (No. 2013ZCX03-01), and General Project of Scientific Research of the Education Department of Liaoning Province (No. L2015547).

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Authors and Affiliations

  1. State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, 110819, China

    Hong-Wei Jia & Jun Zhao

  2. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, China

    Hong-Wei Jia & Jun Zhao

  3. Normal College, Shenyang University, Shenyang, 110044, China

    Hong-Wei Jia

Authors
  1. Hong-Wei Jia
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  2. Jun Zhao
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Corresponding author

Correspondence to Jun Zhao.

Additional information

Recommended by Associate Editor Wing Cheong Dahiel Ho

Hong-Wei Jia received the B. Sc. degree in mathematics from Liaoning Normal University, China in 1996, and received the M. Sc. degree in mathematics from Jilin University, China in 2007. She is now a Ph.D. degree candidate in control theory and applications at the College of Information Science and Engineering, Northeastern University, China.

Her research interests include switched systems, multi-agent systems and distributed control.

Jun Zhao received Ph.D. degree in control theory and applications at Northeastern University, China in 1991. From 1992 to 1993, he was a postdoctoral fellow at the same University. Since 1994, as a professor, he has been with College of Information Science and Engineering, Northeastern University, China. From 1998 to 1999, he was a senior visiting scholar at the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, USA. From November 2003 to May 2005, he was a research fellow at Department of Electronic Engineering, City University of Hong Kong. During 2007 to 2010, he was a fellow at School of Engineering, The Australian National University, Australia.

His research interests include switched systems, nonlinear systems and network synchronization.

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Jia, HW., Zhao, J. Output regulation of multiple heterogeneous switched linear systems. Int. J. Autom. Comput. 15, 492–499 (2018). https://doi.org/10.1007/s11633-017-1058-y

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  • DOI: https://doi.org/10.1007/s11633-017-1058-y

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