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Efficient Convex Optimization for Linear MPC

  • Stephen J. Wright
Chapter
Part of the Control Engineering book series (CONTRENGIN)

Abstract

MPC formulations with linear dynamics and quadratic objectives can be solved efficiently by using a primal-dual interior-point framework, with complexity proportional to the length of the horizon. An alternative, which is more able to exploit the similarity of the problems that are solved at each decision point of linear MPC, is to use an active-set approach, in which the MPC problem is viewed as a convex quadratic program that is parametrized by the initial state \(x_{0}\). Another alternative is to identify explicitly polyhedral regions of the space occupied by \(x_{0}\) within which the set of active constraints remains constant, and to pre-calculate solution operators on each of these regions. All these approaches are discussed here.

References

  1. 1.
    Bemporad, A., Borrelli, F., Morari, M.: Model predictive control based on linear programming—the explicit solution. IEEE Trans. Autom. Control 47(12), 1974–1985 (2002)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bemporad, A., Morari, M., Dua, V., Pistikopoulos, E.N.: The explicit linear quadratic regulator for constrained systems. Automatica 38, 3–20 (2002)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ferreau, H.J.: An online active set strategy for fast solution of parametric quadratic programs with applications to predictive engine control. Ph.D. thesis, Ruprecht-Karls-Universit at Heidelberg Fakult at fur Mathematik und Informatik (2006)Google Scholar
  4. 4.
    Ferreau, H.J., Bock, H.G., Diehl, M.: An online active set strategy to overcome the limitations of explicit MPC. Int. J. Robust Nonlinear Control 18(8), 816–830 (2008)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Ferreau, H.J., Kirches, C., Potschka, A., Bock, H.G., Diehl, M.: qpOASES: a parametric active-set algorithm for quadratic programming. Math. Program. Comput. 6(4), 327–363 (2014)Google Scholar
  6. 6.
    Ferreau, H.J., Potschka, A., Kirches, C.: qpOASES webpage. http://www.qpOASES.org/ (2007–2017)
  7. 7.
    Gertz, E.M., Wright, S.J.: OOQP. http://www.cs.wisc.edu/~swright/ooqp/
  8. 8.
    Gertz, E.M., Wright, S.J.: Object-oriented software for quadratic programming. ACM Trans. Math. Softw. 29, 58–81 (2003)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Pannocchia, G., Rawlings, J.B., Wright, S.J.: Fast, large-scale model predictive control by partial enumeration. Automatica 43, 852–860 (2007)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Pannocchia, G., Wright, S.J., Rawlings, J.B.: Partial enumeration MPC: robust stability results and application to an unstable CSTR. J. Process Control 21, 1459–1466 (2011)CrossRefGoogle Scholar
  11. 11.
    Rao, C.V., Wright, S.J., Rawlings, J.B.: Application of interior-point methods to model predictive control. J. Optim. Theory Appl. 99, 723–757 (1998)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Tondel, P., Johansen, T.A., Bemporad, A.: Evaluation of piecewise affine control via binary search tree. Automatica 39(5), 945–950 (2003)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Wright, S.J.: Applying new optimization algorithms to model predictive control. In: Kantor, J.C. (ed.) Chemical Process Control-V, AIChE Symposium Series, vol. 93, pp. 147–155. CACHE Publications, Austin (1997)Google Scholar
  14. 14.
    Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM Publications, Philadelphia (1997)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Computer Sciences DepartmentUniversity of WisconsinMadisonUSA

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