Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Robust Model Predictive Control

  • Saša V. RakovićEmail author
Living reference work entry

Latest version View entry history

DOI: https://doi.org/10.1007/978-1-4471-5102-9_2-3

Abstract

Model predictive control (MPC) is indisputably one of the rare modern control techniques that has significantly affected control engineering practice due to its natural ability to systematically handle constraints and optimize performance. Robust MPC is an improved form of MPC that is intrinsically robust in the face of uncertainty. The main goal of robust MPC is to devise an optimization-based control synthesis method that accounts for the intricate interactions of the uncertainty with the system, constraints, and performance criteria in a theoretically rigorous and computationally tractable way.

Keywords

Model predictive control Robust model predictive control Robust optimal control Robust stability 
This is a preview of subscription content, log in to check access.

Bibliography

  1. Artstein Z, Raković SV (2008) Feedback and invariance under uncertainty via set iterates. Automatica 44(2):520–525MathSciNetCrossRefGoogle Scholar
  2. Calafiore GC, Campi MC (2006) The scenario approach to robust control design. IEEE Trans Autom Control 51:742–753MathSciNetCrossRefGoogle Scholar
  3. Calafiore GC, Fagaino L (2013) Robust model predictive control via scenario optimization. IEEE Trans Autom Control 56:219–224MathSciNetCrossRefGoogle Scholar
  4. Chisci L, Rossiter JA, Zappa G (2001) Systems with persistent disturbances: predictive control with restricted constraints. Automatica 37:1019–1028MathSciNetCrossRefGoogle Scholar
  5. Goulart PJ, Kerrigan EC, Maciejowski JM (2006) Optimization over state feedback policies for robust control with constraints. Automatica 42(4):523–533MathSciNetCrossRefGoogle Scholar
  6. Grimm G, Messina MJ, Tuna SE, Teel AR (2004) Examples when nonlinear model predictive control is nonrobust. Automatica 40:1729–1738MathSciNetCrossRefGoogle Scholar
  7. Kolmanovsky IV, Gilbert EG (1998) Theory and computation of disturbance invariant sets for discrete time linear systems. Math Probl Eng: Theory Methods Appl 4:317–367CrossRefGoogle Scholar
  8. Langson W, Chryssochoos I, Raković SV, Mayne DQ (2004) Robust model predictive control using tubes. Automatica 40:125–133MathSciNetCrossRefGoogle Scholar
  9. Limon D, Alamo T, Raimondo DM, noz de la Peña DM, Bravo JM, Ferramosca A, Camacho EF (2009) Input-to-state stability: a unifying framework for robust model predictive control. In: Lecture notes in control and information sciences – nonlinear model predictive control: towards new challenging applications, vol 384.zbMATHGoogle Scholar
  10. Löfberg J (2003) Minimax approaches to robust model predictive control. Ph.D. dissertation, Department of Electrical Engineering, Linköping University, Linköping, SwedenGoogle Scholar
  11. Lucia S, Finkler T, Basak D, Engell S (2012) Robust model predictive control by scenario–based multi–stage optimization. In: Proceedings of the 5th international conference on high performance scientific computing, Hanoi, Vietnam.Google Scholar
  12. Mayne DQ, Seron M, Raković SV (2005) Robust model predictive control of constrained linear systems with bounded disturbances. Automatica 41:219–224MathSciNetCrossRefGoogle Scholar
  13. Mayne DQ, Raković SV, Findeisen R, Allgöwer F (2006) Robust output feedback model predictive control of constrained linear systems. Automatica 42:1217–122MathSciNetCrossRefGoogle Scholar
  14. Mayne DQ, Raković SV, Findeisen R, Allgöwer F (2009) Robust output feedback model predictive control of constrained linear systems: time varying case. Automatica 45:2082–2087MathSciNetCrossRefGoogle Scholar
  15. Raković SV (2015) Robust model–predictive control. In: Baillieul J, Samad T (eds) Encyclopedia of systems and control. Springer, London, pp 1225–1233CrossRefGoogle Scholar
  16. Raković SV (2009) Set theoretic methods in model predictive control. In: Lecture notes in control and information sciences – nonlinear model predictive control: towards new challenging applications, vol 384, pp 41–54CrossRefGoogle Scholar
  17. Raković SV (2012) Invention of prediction structures and categorization of robust mpc syntheses. In: Proceedings of the IFAC conference on nonlinear model predictive control NMPC 2012, Noordwijkerhout, the Netherlands, , Plenary PaperGoogle Scholar
  18. Raković SV, Kouvaritakis B, Findeisen R, Cannon M (2012) Homothetic tube model predictive control. Automatica 48:1631–1638MathSciNetCrossRefGoogle Scholar
  19. Raković SV, Kouvaritakis B, Cannon M, Panos C, Findeisen R (2012) Parameterized tube model predictive control. IEEE Trans Autom Control 57:2746–2761MathSciNetCrossRefGoogle Scholar
  20. Raković SV, Kouvaritakis B, Cannon M (2013) Equi–normalization and exact scaling dynamics in homothetic tube model predictive control. Syst Control Lett 62(2):209–217MathSciNetCrossRefGoogle Scholar
  21. Raković SV, Levine WS, Açikmeşe B (2016) Elastic tube model predictive control. In: Proceedings of the 2016 American control conference (ACC), Boston, MA, USAGoogle Scholar
  22. Rawlings JB, Mayne DQ (2009) Model predictive control: theory and design. Nob Hill Publishing, MadisonGoogle Scholar
  23. Scokaert POM, Mayne DQ (1998) Min–max feedback model predictive control for constrained linear systems. IEEE Trans Autom Control 43:1136–1142MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  1. 1.School of AutomationBeijing Institute of TechnologyBeijingChina

Section editors and affiliations

  • James B. Rawlings
    • 1
  1. 1.Dept. of Chemical EngineeringUniversity of CaliforniaSanta BarbaraUSA