Skip to main content

Distributed Event-Based Control for Interconnected Linear Systems

  • Chapter
  • First Online:
Contributions to Networked and Event-Triggered Control of Linear Systems

Part of the book series: Springer Theses ((Springer Theses))

  • 577 Accesses

Abstract

This chapter presents a distributed event-based control (DEBC) strategy for a networked dynamical system consisting of N linear time-invariant interconnected subsystems. Each subsystem broadcasts its state over the network according to certain triggering rules which depend on local information only. The system can converge asymptotically to the equilibrium under the proposed control design, and the existence of a lower bound for the broadcasting period is guaranteed. The problem is solved assuming that the control law is able to decouple the subsystems and a continuous time system, and the results are extended to non-perfect decoupling and discrete-time systems afterwards.

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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.

    Decentralized control neglects the interaction between the subsystems and designs a local controller for each subsystem, whereas the local regulators exchange information among them in distributed control.

References

  1. Al-Mohi A, Higham NJ (2009) Computing the Fréchet derivative of the matrix exponential, with an application to condition number estimate. SIAM J Matrix Anal Appl 30:1639–1657

    Article  MATH  Google Scholar 

  2. Bauer FL, Fike CT (1960) Norms and exclusion theorems. Numer Math 2:137–141

    Article  MathSciNet  MATH  Google Scholar 

  3. Chu KWE (1986) Generalization of the Bauer-Fike theorem. Numer Math 49:685–691

    Google Scholar 

  4. De Persis C, Sailer R, Wirth F (2011) On a small-gain approach to distributed event-triggered control. In: Proceedings of the 18th IFAC world congress. Milano, pp 2401–2406

    Google Scholar 

  5. Diaz-Guilera A, Arenas A (2008) Phase patterns of coupled oscillators with application to wireless communication. Bio-inspired computing and communication. Springer, Berlin

    Google Scholar 

  6. Dimarogonas DV, Frazzoli E, Johansson KH (2012) Distributed event-triggered control for multi-agent systems. IEEE Trans Autom Control 57(5):1291–1297

    Article  MathSciNet  Google Scholar 

  7. Franklin GF, Powell JD, Workman M (1997) Digital control of dynamic systems. Addison-Wesley, E.U.A

    MATH  Google Scholar 

  8. Garcia E, Antsaklis PJ (2012) Decentralized model-based event-triggered control of networked systems. In: American control conference. Montreal, pp 6485–6490

    Google Scholar 

  9. Guinaldo M, Dimaragonas DV, Johansson KH, Sánchez J, Dormido S (2011) Distributed event-based control for interconnected linear systems. In: 50th control and decision conference. Orlando, pp 2553–2558

    Google Scholar 

  10. Heemels WPMH, Sandee J, van den Bosch P (2008) Analysis of event-driven controllers for linear systems. Int J Control 81(4):571–590

    Article  MathSciNet  MATH  Google Scholar 

  11. Higham NJ (2008) Functions of matrices: theory and computation. Society for Industrial and Applied Mathematics, Philadelphia

    Book  MATH  Google Scholar 

  12. Horch A, Isaksson AJ (2001) Assessment of the sampling rate in control systems. Control Eng Pract 9:533–544

    Article  Google Scholar 

  13. Kato T (1966) Perturbation theory for linear operators. Springer, Heidelberg

    Google Scholar 

  14. Lunze J, Lehmann D (2010) A state-feedback approach to event-based control. Automatica 46(1):211–215

    Article  MathSciNet  MATH  Google Scholar 

  15. Mazo M, Tabuada P (2011) Decentralized event-triggered control over wireless sensor/actuator networks. IEEE Trans Autom Control 56(10):2456–2461

    Article  MathSciNet  Google Scholar 

  16. Seyboth GS, Dimarogonas DV, Johansson KH (2013) Event-based broadcasting for multi-agent average consensus. Automatica 49(1):245–252

    Article  MathSciNet  MATH  Google Scholar 

  17. Stefanovska A (2007) Coupled oscillators: complex but not complicated cardiovascular and brain interactions. IEEE Eng Med Biol Mag 26(6):25–29

    Article  Google Scholar 

  18. Van Loan CF (1977) The sensitivity of the matrix exponential. SIAM J Numer Anal 14(6):971–981

    Article  MathSciNet  MATH  Google Scholar 

  19. Wang X, Lemmon MD (2008) Event-triggered broadcasting across distributed networked control systems. In: American control conference. Seattle, pp 3139–3144

    Google Scholar 

  20. Wang X, Lemmon MD (2011) Event-triggering in distributed networked control systems. IEEE Trans Autom Control 56(3):586–601

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to María Guinaldo Losada .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Guinaldo Losada, M. (2016). Distributed Event-Based Control for Interconnected Linear Systems. In: Contributions to Networked and Event-Triggered Control of Linear Systems. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-34081-4_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-34081-4_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-34080-7

  • Online ISBN: 978-3-319-34081-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics