Skip to main content

Sequential Monte Carlo for Model Predictive Control

  • Chapter
Nonlinear Model Predictive Control

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

Abstract

This paper proposes the use of Sequential Monte Carlo (SMC) as the computational engine for general (non-convex) stochastic Model Predictive Control (MPC) problems. It shows how SMC methods can be used to find global optimisers of non-convex problems, in particular for solving open-loop stochastic control problems that arise at the core of the usual receding-horizon implementation of MPC. This allows the MPC methodology to be extended to nonlinear non-Gaussian problems. We illustrate the effectiveness of the approach by means of numerical examples related to coordination of moving agents.

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. Amzal, B., Bois, F.Y., Parent, E., Robert, C.P.: Bayesian-Optimal Design via Interacting Particle systems. Journal of the American Statistical Association, Theory and Methods 101(474) (2006)

    Google Scholar 

  2. Andrieu, C., Doucet, A., Singh, S.S., Tadić, V.: Particle Methods for Change Detection, Identification and Control. Proceedings of the IEEE 92, 423–438 (2004)

    Article  Google Scholar 

  3. Bertsekas, D.P.: Dynamic programming and optimal control. Athena Scientific, Belmont (1995)

    MATH  Google Scholar 

  4. Bertsekas, D.P.: Dynamic Programming and Suboptimal Control: A Survey from ADP to MPC. European J. of Control 11(4-5) (2005)

    Google Scholar 

  5. Del Moral, P.: Feynman-Kac formulae: genealogical and interacting particlesystems with applications. Springer, New York (2004)

    Google Scholar 

  6. Del Moral, P., Doucet, A., Jasra, A.: Sequential Monte Carlo Samplers. J. Royal Statist. Soc. B 68(3), 411–436 (2006)

    Article  MATH  Google Scholar 

  7. Doucet, A., de Freitas, J.F.G., Gordon, N.J.: Sequential Monte Carlo Methods in Practice. Springer, New York (2001)

    MATH  Google Scholar 

  8. Hwang, C.R.: Laplace’s method revisited: weak convergence of probability measures. Ann. Probab. 8(6), 1177–1182 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  9. Johansen, A.M., Doucet, A., Davy, M.: Particle methods for Maximum Likelihood Parameter Estimation in Latent Variable Models. Statistics and Computing 18(1), 47–57 (2008)

    Article  MathSciNet  Google Scholar 

  10. Lecchini Visintini, A., Glover, W., Lygeros, J., Maciejowski, J.M.: Monte carlo optimization for conflict resolution in air traffic control. IEEE Trans. Intell. Transp. Syst. 7(4), 470–482 (2006)

    Article  Google Scholar 

  11. Lecchini Visintini, A., Lygeros, J., Maciejowski, J.M.: Simulated Annealing: Rigorous finite-time guarantees for optimization on continuous domains. In: Platt, J.C., Koller, D., Singer, Y., Roweis, S. (eds.) Advances in NIPS 20, pp. 865–872. MIT Press, Cambridge (2008)

    Google Scholar 

  12. Maciejowski, J.M.: Predictive control with Constraints. Prentice-Hall, Englewood Cliffs (2002)

    Google Scholar 

  13. Muller, P., Sanso, B.G., De Iorio, M.: Optimal Bayesian design by Inhomogeneous Markov Chain Simulation. Journal of the American Statistical Association, 788–798 (2004)

    Google Scholar 

  14. Rawlings, J.B., Bakshi, B.R.: Particle filtering and moving horizon estimation. Comput. Chem. Eng. 30, 1529–1541 (2006)

    Article  Google Scholar 

  15. Robert, C.P., Casella, G.: Monte Carlo Statistical Methods, 2nd edn. Springer, Heidelberg (2004)

    MATH  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

Kantas, N., Maciejowski, J.M., Lecchini-Visintini, A. (2009). Sequential Monte Carlo for Model Predictive Control. 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_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-01094-1_21

  • 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