Skip to main content

Stochastic Model Predictive Control

  • Reference work entry
  • First Online:
Encyclopedia of Systems and Control

Abstract

Model predictive control (MPC) is a control strategy that has been used successfully in numerous and diverse application areas. The aim of the present entry is to discuss how the basic ideas of MPC can be extended to problems involving random model uncertainty with known probability distribution. We discuss cost indices, constraints, closed-loop properties, and implementation issues.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 899.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
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

Similar content being viewed by others

Bibliography

  • Åström KJ, Wittenmark B (1973) On self tuning regulators. Automatica 9(2):185–199

    Google Scholar 

  • Calafiore GC, Campi MC (2005) Uncertain convex programs: randomized solutions and confidence levels. Math Program 102(1):25–46

    MathSciNet  Google Scholar 

  • Calafiore GC, Fagiano L (2013) Robust model predictive control via scenario optimization. IEEE Trans Autom Control 58(1):219–224

    MathSciNet  Google Scholar 

  • Cannon M, Cheng Q, Kouvaritakis B, Rakovic SV (2012) Stochastic tube MPC with state estimation. Automatica 48(3):536–541

    MathSciNet  Google Scholar 

  • Charnes A, Cooper WW (1963) Deterministic equivalents for optimizing and satisficing under chance constraints. Oper Res 11(1):19–39

    MathSciNet  Google Scholar 

  • Evans M, Cannon M, Kouvaritakis B (2012) Robust MPC for linear systems with bounded multiplicative uncertainty. In: IEEE conference on decision and control, Maui, pp 248–253

    Google Scholar 

  • Kouvaritakis B, Cannon M, Raković SV, Cheng Q (2010) Explicit use of probabilistic distributions in linear predictive control. Automatica 46(10):1719–1724

    MathSciNet  Google Scholar 

  • Lee JH, Cooley BL (1998) Optimal feedback control strategies for state-space systems with stochastic parameters. IEEE Trans Autom Control 43(10):1469–1475

    MathSciNet  Google Scholar 

  • Lee JH, Yu Z (1997) Worst-case formulations of model predictive control for systems with bounded parameters. Automatica 33(5):763–781

    MathSciNet  Google Scholar 

  • Marruedo DL, Alamo T, Camacho EF (2002) Input-to-state stable MPC for constrained discrete-time nonlinear systems with bounded additive uncertainties. In: IEEE conference on decision and control, Las Vegas, pp 4619–4624

    Google Scholar 

  • Mayne DQ, Seron MM, Raković SV (2005) Robust model predictive control of constrained linear systems with bounded disturbances. Automatica 41(2):219–224

    MathSciNet  Google Scholar 

  • Primbs JA, Sung CH (2009) Stochastic receding horizon control of constrained linear systems with state and control multiplicative noise. IEEE Trans Autom Control 54(2):221–230

    MathSciNet  Google Scholar 

  • Schwarm AT, Nikolaou M (1999) Chance-constrained model predictive control. AIChE J 45(8):1743–1752

    Google Scholar 

  • Stoorvogel AA, Weiland S, Batina I (2007) Model predictive control by randomized algorithms for systems with constrained inputs and stochastic disturbances. http://wwwhome.math.utwente.nl/~stoorvogelaa/subm01.pdf

  • van Hessem DH, Bosgra OH (2002) A conic reformulation of model predictive control including bounded and stochastic disturbances under state and input constraints. In: IEEE conference on decision and control, Las Vegas, pp 4643–4648

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag London

About this entry

Cite this entry

Kouvaritakis, B., Cannon, M. (2015). Stochastic Model Predictive Control. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5058-9_7

Download citation

Publish with us

Policies and ethics