Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Explicit Model Predictive Control

  • PhDAlberto Bemporad
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_10-1

Abstract

Model predictive control (MPC) has been used in the process industries for more than 30 years because of its ability to control multivariable systems in an optimized way under constraints on input and output variables. Traditionally, MPC requires the solution of a quadratic program (QP) online to compute the control action, often restricting its applicability to slow processes. Explicit MPC completely removes the need for on-line solvers by precomputing the control law off-line, so that online operations reduce to a simple function evaluation. Such a function is piecewise affine in most cases, so that the MPC controller is equivalently expressed as a lookup table of linear gains, a form that is extremely easy to code, requires only basic arithmetic operations, and requires a maximum number of iterations that can be exactly computed a priori.

Keywords

Model predictive control Quadratic programming Embedded optimization Multiparametric programming Constrained control 
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References

  1. Alessio A, Bemporad A (2009) A survey on explicit model predictive control. In: Magni L, Raimondo DM, Allgower F (eds) Nonlinear model predictive control: towards new challenging applications. Lecture notes in control and information sciences, vol 384. Springer, Berlin/Heidelberg, pp 345–369CrossRefGoogle Scholar
  2. Baotić M (2002) An efficient algorithm for multi-parametric quadratic programming. Tech. Rep. AUT02-05, Automatic Control Institute, ETH, ZurichGoogle Scholar
  3. Bemporad A (2003) Hybrid toolbox – user’s guide. http://cse.lab.imtlucca.it/~bemporad/hybrid/toolbox
  4. Bemporad A, Borrelli F, Morari M (2000) Piecewise linear optimal controllers for hybrid systems. In: Proceedings of American control conference, Chicago, pp 1190–1194Google Scholar
  5. Bemporad A, Borrelli F, Morari M (2002a) Model predictive control based on linear programming – the explicit solution. IEEE Trans Autom Control 47(12):1974–1985CrossRefMathSciNetGoogle Scholar
  6. Bemporad A, Morari M, Dua V, Pistikopoulos E (2002b) The explicit linear quadratic regulator for constrained systems. Automatica 38(1):3–20CrossRefMATHMathSciNetGoogle Scholar
  7. Bemporad A, Borrelli F, Morari M (2003) Min-max control of constrained uncertain discrete-time linear systems. IEEE Trans Autom Control 48(9):1600–1606CrossRefMathSciNetGoogle Scholar
  8. Bemporad A, Morari M, Ricker N (2014) Model predictive control toolbox for matlab – user’s guide. The Mathworks, Inc., http://www.mathworks.com/access/helpdesk/help/toolbox/mpc/
  9. Borrelli F, Baotić M, Bemporad A, Morari M (2005) Dynamic programming for constrained optimal control of discrete-time linear hybrid systems. Automatica 41(10):1709–1721CrossRefMATHMathSciNetGoogle Scholar
  10. Borrelli F, Bemporad A, Morari M (2011, in press) Predictive control for linear and hybrid systems. Cambridge University PressGoogle Scholar
  11. Geyer T, Torrisi F, Morari M (2008) Optimal complexity reduction of polyhedral piecewise affine systems. Automatica 44:1728–1740CrossRefMATHMathSciNetGoogle Scholar
  12. Jones C, Morari M (2006) Multiparametric linear complementarity problems. In: Proceedings of the 45th IEEE conference on decision and control, San Diego, pp 5687–5692Google Scholar
  13. Kvasnica M, Grieder P, Baotić M (2006) Multi parametric toolbox (MPT). http://control.ee.ethz.ch/~mpt/
  14. Mayne D, Rawlings J (2009) Model predictive control: theory and design. Nob Hill Publishing, LCC, MadisonGoogle Scholar
  15. Patrinos P, Bemporad A (2014) An accelerated dual gradient-projection algorithm for embedded linear model predictive control. IEEE Trans Autom Control 59(1):18–33CrossRefGoogle Scholar
  16. Patrinos P, Sarimveis H (2010) A new algorithm for solving convex parametric quadratic programs based on graphical derivatives of solution mappings. Automatica 46(9):1405–1418CrossRefMATHMathSciNetGoogle Scholar
  17. Ricker N (1985) Use of quadratic programming for constrained internal model control. Ind Eng Chem Process Des Dev 24(4):925–936CrossRefGoogle Scholar
  18. Spjøtvold J, Kerrigan E, Jones C, Tøndel P, Johansen TA (2006) On the facet-to-facet property of solutions to convex parametric quadratic programs. Automatica 42(12):2209–2214CrossRefMathSciNetGoogle Scholar
  19. Tøndel P, Johansen TA, Bemporad A (2003) An algorithm for multi-parametric quadratic programming and explicit MPC solutions. Automatica 39(3):489–497CrossRefMathSciNetGoogle Scholar
  20. Tøndel P, Johansen TA, Bemporad A (2003b) Evaluation of piecewise affine control via binary search tree. Automatica 39(5):945–950CrossRefMathSciNetGoogle Scholar
  21. Wang Y, Boyd S (2010) Fast model predictive control using online optimization. IEEE Trans Control Syst Technol 18(2):267–278CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.IMT Institute for Advanced Studies LuccaLuccaItaly