Skip to main content

An NMPC Approach to Avoid Weakly Observable Trajectories

  • Chapter
Nonlinear Model Predictive Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 384))

Abstract

Nonlinear systems can be poorly or non-observable along specific state and output trajectories or in certain regions of the state space. Operating the system along such trajectories or in such regions can lead to poor state estimates being provided by an observer. Such trajectories should be avoided if used for state feedback control or monitoring purposes. In this paper, we outline a possible approach to avoid weakly observable trajectories in the frame of nonlinear model predictive control (NMPC). To illustrate the practical relevance and applicability, the proposed controller is used for an emergency collision avoidance maneuver for passenger cars.

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 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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Antonov, S., Fehn, A., Kugi, A.: Ein neuartiger Ansatz zur Querdynamikregelung von Personenkraftwagen (A new approach to lateral dynamics control of passenger vehicles). at-Automatisierungstechnik 55(9), 488–496 (2007)

    Article  Google Scholar 

  2. Böhm, C., Findeisen, R., Allgöwer, F.: Avoidance of poorly observable trajectories: A predictive control perspective. In: Proceedings of the 17th IFAC World Congress, Seoul, pp. 1952–1957 (2008)

    Google Scholar 

  3. Böhm, C., Raff, T., Findeisen, R., Allgöwer, F.: Calculating the terminal region for Lure systems via LMIs. In: Proceedings of the American Control Conference, Seattle, pp. 1127–1132 (2008)

    Google Scholar 

  4. Brandin, V.N., Kostyukovskii, Y.M.L., Razorenov, G.N.: Global observability conditions for nonlinear dynamic systems. Automation and Remote Control 36, 1585–1591 (1976)

    MathSciNet  Google Scholar 

  5. Falcone, P., Borrelli, F., Asgari, J., Tseng, H.E., Hrovat, D.: Predictive active steering control for autonomous vehicle systems. IEEE Transactions on Control Systems Technology 15(3), 566–580 (2007)

    Article  Google Scholar 

  6. Fontes, F.A.: A general framework to design stabilizing nonlinear model predictive controllers. System and Control Letters 42(2), 127–142 (2000)

    Article  MathSciNet  Google Scholar 

  7. Heß, F.: Autonomous vehicle collision avoidance with predictive control. Diploma thesis, University of Stuttgart (2008)

    Google Scholar 

  8. Imsland, L., Johansen, T.A., Fossen, T.I., Fjær Grip, H., Kalkkuhl, J.C., Suissa, A.: Vehicle velocity estimation using nonlinear observers. Automatica 42(12), 2091–2103 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  9. Krener, A.J.: Nonlinear stabilizability and detectability. In: Helmke, U., Mennicken, R., Saurer, J. (eds.) Systems and Networks: Mathematical Theory and Applications, pp. 231–250 (1994)

    Google Scholar 

  10. Litz, L.: Modale Maße für Steuerbarkeit, Beobachtbarkeit, Regelbarkeit und Dominanz - Zusammenhänge, Schwachstellen, neue Wege. Regelungstechnik 31, 148–158 (1983)

    MATH  Google Scholar 

  11. Nijmeijer, H., van der Schaft, A.: Nonlinear Dynamical Control Systems. Springer, Heidelberg (1990)

    MATH  Google Scholar 

  12. Pacejka, H.B., Bakker, E.: The magic formula tyre model. Vehicle System Dynamics 21, 1–18 (2004)

    Article  Google Scholar 

  13. Vargas, A.: Observer Design for Nonlinear Systemes with Reduced Observability Properties. PhD thesis, University of Stuttgart (2003)

    Google Scholar 

  14. Zanten, V.A.T.: Bosch ESP systems: 5 years of experience. SAE Technical Paper No. 2000-01-1633 (2000)

    Google Scholar 

  15. Zeitz, M., Xia, X.: On nonlinear continuous observers. International Journal of Control 66(6), 943–954 (1997)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Böhm, C., Heß, F., Findeisen, R., Allgöwer, F. (2009). An NMPC Approach to Avoid Weakly Observable Trajectories. In: Magni, L., Raimondo, D.M., Allgöwer, F. (eds) Nonlinear Model Predictive Control. Lecture Notes in Control and Information Sciences, vol 384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01094-1_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-01094-1_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01093-4

  • Online ISBN: 978-3-642-01094-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics