Skip to main content

Adaptive Internal Model-Based Distributed Output Agreement in a Class of Multi-Agent Dynamic Systems

  • Chapter
  • First Online:
Complex Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 55))

  • 1463 Accesses

Abstract

In this study we consider the distributed output agreement problem in a class of multi-agent dynamic systems with uncertainties. The problem is formulated as a nonlinear servomechanism problem and an adaptive internal model-based controller is used to achieve agreement of the agent outputs using local information. Various agent neighborhood topologies are considered and the performance of the system is verified using simple numerical simulations.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Here we use the term connected loosely meaning that at least minimum connectivity conditions are satisfied and there are no agents or groups of agents which are disconnected from the rest of the multi-agent system. For example, as mentioned earlier for static unidirectional topology it is sufficient that the interaction topology has a spanning tree.

  2. 2.

    At the time the simulation is stopped, the average interagent distance is very close to zero and continues to decrease.

References

  1. Byrnes, C.I., Priscoli, F.D., Isidori, A., Kang, W.: Structurally stable output regulation of nonlinear systems. Automatica 33(3), 369–385 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chen, X., Serrani, A., Özbay, H.: Control of leader-follower formations of terrestrial uavs. In: Proceedings of the 42nd IEEE Conference on Decision and Control, pp. 498–503. Hawaii, USA, Dec 2003

    Google Scholar 

  3. Davison, E.J.: The robust control of a servomechanism problem for linear time-invariant multivariable systems. IEEE Trans. Autom. Control 21(1), 25–34 (1976)

    Google Scholar 

  4. Francis, B.A.: The linear multivariable regulator problem. In: 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes, vol. 15, pp. 873–878 (1976)

    Google Scholar 

  5. Francis, B.A., Wonham, W.M.: The internal model principle of control theory. Automatica 12, 457–465 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gazi, V., Fidan, B.: Coordination and control of multi-agent dynamic systems: models and approaches. In: Sahin, E., Spears, W.M., Winfield, A.F.T. (eds.) Proceedings of the SAB06 Workshop on Swarm Robotics, pp. 71–102. Lecture Notes in Computer Science (LNCS) vol. 4433, Springer, Berlin (2007)

    Google Scholar 

  7. Gazi, V.: Formation control of a multi-agent system using nonlinear servomechanism. Int. J. Control 78(8), 554–565 (2005)

    Google Scholar 

  8. Gazi, V.: Output regulation of a class of linear systems with switched exosystems. Int. J. Control 80(10), 1665–1675 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Gazi, V.: Stability of a discrete-time asynchronous swarm with time-dependent communication links. IEEE Trans. Syst. Man Cybern: Part B 38(1), 267–274 (2008)

    Article  Google Scholar 

  10. Gazi, V., Passino, K.M.: Decentralized output regulation of a class of nonlinear systems. Int. J. Control 79(12), 1512–1522 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gazi, V., Passino, K.M.: Swarm Stability and Optimization. Springer, Heidelberg (2011)

    Book  MATH  Google Scholar 

  12. Gül, E., Gazi, V.: Adaptive internal model based distributed output agreement in a class of multi-agent dynamic systems. In: Kolemisevska-Gugulovska, T.D., Stankovski, M.J. (eds.) Proceedings of the Special International Conference on Complex Systems: Synergy of Control, Computing, and Communications (COSY 2011), pp. 215–222. The Society for Electronics, Telecommunications, Automation, and Informatics of Macedonia, Skopje, MK, Ohrid, Macedonia, Sept 2011

    Google Scholar 

  13. Gül, E., Gazi, V.: Adaptive internal model based formation control of a class of multi-agent systems with switched exosystems. In: Chinese Control and Decision Conference, pp. 6–13. Taiyuan, China, May 2012

    Google Scholar 

  14. Gül, E., Gazi, V.: Adaptive internal model based formation control of a class of multi-agent systems. In: American Control Conference, pp. 4800–4805. Baltimore, MD, USA, June–July 2010

    Google Scholar 

  15. Huang, J., Lin, C.: On a robust nonlinear servomechanism problem. IEEE Trans. Autom. Control 39(7), 1510–1513 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  16. Huang, J., Rugh, W.J.: On a nonlinear multivariable servomechanism problem. Automatica 26(6), 963–972 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  17. Isidori, A., Byrnes, C.I.: Output regulation of nonlinear systems. IEEE Trans. Autom. Control 35(2), 131–140 (1990)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  19. Khalil, H.K.: Robust servomechanism output feedback controllers for feedback linearizable systems. Automatica 30(10), 1587–1599 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  20. Kim, H., Shim, H., Seo, J.H.: Output consensus of heterogeneous uncertain linear multi-agent systems. IEEE Trans. Autom. Control 56(1), 200–206 (2011)

    Article  MathSciNet  Google Scholar 

  21. Lin, Z., Francis, B., Maggiore, M.: Necessary and sufficient graphial conditions for formation control of unicycles. IEEE Trans. Autom. Control 50(1), 121–127 (2005)

    Article  MathSciNet  Google Scholar 

  22. Mahmoud, N.A., Khalil, H.K.: Asymptotic regulation of minimum phase nonlinear systems using output feedback. IEEE Trans. Autom. Control 40(10), 1402–1412 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  23. Mahmoud, N.A., Khalil, H.K.: Robust control for a nonlinear servomechanism problem. Int. J. Control 66(6), 779–802 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  24. Marino, R., Tomei, P.: Output regulation for linear systems via adaptive internal model. IEEE Trans. Autom. Control 48(12), 2199–2202 (2003)

    Article  MathSciNet  Google Scholar 

  25. Moreau, L.: Stability of multiagent systems with time-dependent communication links. IEEE Tran. Autom. Control 50(2), 169–182 (2005)

    Article  MathSciNet  Google Scholar 

  26. Nikiforov, V.O.: Adaptive nonlinear tracking with complete compensation of unknown disturbances. Euro. J. Control 4, 132–139 (1998)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  28. Ren, W., Beard, R.W.: Consensus seeking in multi-agent systems under dynamically changing interaction topologies. IEEE Trans. Autom. Control 50(5), 655–661 (2005)

    Article  MathSciNet  Google Scholar 

  29. Şamiloğlu, A.T., Gazi, V., Koku, A.B.: Asynchronous cyclic pursuit. In: S. Nolfi (ed.) Proceedings of 9’th Conference on Simulation of Adaptive Behavior (SAB06), pp. 667–678. Lecture Notes in Artificial Intelligence (LNAI) 4095, Springer, Berlin (2006)

    Google Scholar 

  30. Serrani, A., Isidori, A., Marconi, L.: Semiglobal nonlinear output regulation with adaptive internal model. IEEE Trans. Autom. Control 46(8), 1178–1194 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  31. Serrani, A., Isidori, A.: Global robust output regulation for a class of nonlinear systems. Syst./Control Lett. 39, 133–139 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  32. Wieland, P., Allgöwer, F.: An internal model principle for consensus in heterogeneous linear multi-agent systems. In: 1st IFAC Workshop on Estimation and Control in Networked Systems, pp. 7–12. Venice, Italy, Sept 2009

    Google Scholar 

  33. Wieland, P., Allgöwer, F.: An internal model principle for synchronization. In: IEEE International Conference on Control and Automation (ICCA), pp. 285–290. Christchurch, New Zealand, Dec 2009

    Google Scholar 

  34. Wieland, P., Sepulchre, R., Allgöwer, F.: An internal model principle is necessary and sufficient for linear output synchronization. Automatica 47(5), 1068–1074 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  35. Xiang, J., Wei, W., Li, Y.: Synchronized output regulation of linear networked systems. IEEE Trans. Autom. Control 54(6), 1336–1341 (2009)

    Article  MathSciNet  Google Scholar 

  36. Ye, X., Huang, J.: Decentralized adaptive output regulation for a class of large-scale nonlinear systems. IEEE Tran. Autom. Control 48(2), 276–281 (2003)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) under grant no 109E175.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Veysel Gazi .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Gül, E., Gazi, V. (2016). Adaptive Internal Model-Based Distributed Output Agreement in a Class of Multi-Agent Dynamic Systems. In: Dimirovski, G. (eds) Complex Systems. Studies in Systems, Decision and Control, vol 55. Springer, Cham. https://doi.org/10.1007/978-3-319-28860-4_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-28860-4_21

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-28858-1

  • Online ISBN: 978-3-319-28860-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics