Skip to main content

Nonlinear Model Predictive Control

  • Chapter

Part of the Communications and Control Engineering book series (CCE)

Abstract

In this chapter, we introduce the nonlinear model predictive control algorithm in a rigorous way. We start by defining a basic NMPC algorithm for constant reference and continue by formalizing state and control constraints. Viability (or weak forward invariance) of the set of state constraints is introduced and the consequences for the admissibility of the NMPC feedback law are discussed. After having introduced NMPC in a special setting, we describe various extensions of the basic algorithm, considering time varying reference solutions, terminal constraints and costs and additional weights. Finally, we investigate the optimal control problem corresponding to this generalized setting and prove several properties, most notably the dynamic programming principle.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-0-85729-501-9_3
  • Chapter length: 24 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   149.00
Price excludes VAT (USA)
  • ISBN: 978-0-85729-501-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book
USD   199.99
Price excludes VAT (USA)
Fig. 3.1

References

  1. Alamir, M.: Stabilization of Nonlinear Systems Using Receding-horizon Control Schemes. Lecture Notes in Control and Information Sciences, vol. 339. Springer, London (2006)

    MATH  Google Scholar 

  2. Bellman, R.: Dynamic Programming. Princeton University Press, Princeton (1957). Reprinted in 2010

    MATH  Google Scholar 

  3. Bemporad, A., Filippi, C.: Suboptimal explicit MPC via approximate multiparametric quadratic programming. In: Proceedings of the 40th IEEE Conference on Decision and Control – CDC 2001, Orlando, Florida, USA, pp. 4851–4856 (2001)

    Google Scholar 

  4. Bertsekas, D.P.: Dynamic Programming and Optimal Control, vol. I, 3rd edn. Athena Scientific, Belmont (2005)

    Google Scholar 

  5. Bertsekas, D.P.: Dynamic Programming and Optimal Control, vol. II, 2nd edn. Athena Scientific, Belmont (2001)

    Google Scholar 

  6. Borrelli, L., Baotic, T., Bemporad, A., Morari, T.: Efficient on-line computation of constrained optimal control. In: Proceedings of the 40th IEEE Conference on Decision and Control – CDC 2001, Orlando, Florida, USA, pp. 1187–1192 (2001)

    Google Scholar 

  7. Doležal, J.: Existence of optimal solutions in general discrete systems. Kybernetika11(4), 301–312 (1975)

    MathSciNet  MATH  Google Scholar 

  8. Dorato, P., Levis, A.H.: Optimal linear regulators: the discrete-time case. IEEE Trans. Automat. Control16, 613–620 (1971)

    MathSciNet  CrossRef  Google Scholar 

  9. Findeisen, R.: Nonlinear model predictive control: a sampled-data feedback perspective. PhD thesis, University of Stuttgart, VDI-Verlag, Düsseldorf (2004)

    Google Scholar 

  10. Keerthi, S.S., Gilbert, E.G.: An existence theorem for discrete-time infinite-horizon optimal control problems. IEEE Trans. Automat. Control30(9), 907–909 (1985)

    MathSciNet  MATH  CrossRef  Google Scholar 

  11. Tøndel, P., Johansen, T.A., Bemporad, A.: An algorithm for multi-parametric quadratic programming and explicit MPC solutions. Automatica39(3), 489–497 (2003)

    MathSciNet  CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lars Grüne .

Rights and permissions

Reprints and Permissions

Copyright information

© 2011 Springer-Verlag London Limited

About this chapter

Cite this chapter

Grüne, L., Pannek, J. (2011). Nonlinear Model Predictive Control. In: Nonlinear Model Predictive Control. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-501-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-0-85729-501-9_3

  • Publisher Name: Springer, London

  • Print ISBN: 978-0-85729-500-2

  • Online ISBN: 978-0-85729-501-9

  • eBook Packages: EngineeringEngineering (R0)