Skip to main content

Multi-Parametric Toolbox (MPT)

  • Conference paper
Hybrid Systems: Computation and Control (HSCC 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2993))

Included in the following conference series:

Abstract

A Multi-Parametric Toolbox (MPT) for computing optimal or suboptimal feedback controllers for constrained linear and piecewise affine systems is under development at ETH. The toolbox offers a broad spectrum of algorithms compiled in a user friendly and accessible format: starting from different performance objectives (linear, quadratic, minimum time) to the handling of systems with persistent additive disturbances and polytopic uncertainties. The algorithms included in the toolbox are a collection of results from recent publications in the field of constrained optimal control of linear and piecewise affine systems [10,13,4,9,16,17,15,14,7].

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Baotić, M.: An efficient algorithm for multi-parametric quadratic programming. Technical Report AUT02-04, Automatic Control Laboratory, ETH Zurich, Switzerland (February 2002)

    Google Scholar 

  2. Baotić, M., Christophersen, F.J., Morari, M.: Infinite time optimal control of hybrid systems with a linear performance index. In: Proc. of the Conf. on Decision and Control, Maui, Hawaii, USA (December 2003)

    Google Scholar 

  3. Baotić, M., Christophersen, F.J., Morari, M.: A new Algorithm for Constrained Finite Time Optimal Control of Hybrid Systems with a Linear Performance Index. In: European Control Conference, Cambridge, UK (September 2003)

    Google Scholar 

  4. Bemporad, A., Borrelli, F., Morari, M.: Explicit solution of LP-based model predictive control. In: Proc. 39th IEEE Conf. on Decision and Control, Sydney, Australia (December 2000)

    Google Scholar 

  5. Bemporad, A., Borrelli, F., Morari, M.: Optimal controllers for hybrid systems: Stability and piecewise linear explicit form. In: Proc. 39th IEEE Conf. on Decision and Control, Sydney, Australia (December 2000)

    Google Scholar 

  6. Bemporad, A., Borrelli, F., Morari, M.: Min-max control of constrained uncertain discrete-time linear systems. IEEE Trans. Automatic Control 48(9), 1600–1606 (2003)

    Article  MathSciNet  Google Scholar 

  7. Bemporad, A., Fukuda, K., Torrisi, F.D.: Convexity recognition of the union of polyhedra. Computational Geometry 18, 141–154 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bemporad, A., Morari, M., Dua, V., Pistikopoulos, E.N.: The explicit linear quadratic regulator for constrained systems. Automatica 38(1), 3–20 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Borrelli, F.: Constrained Optimal Control Of Linear And Hybrid Systems. Lecture Notes in Control and Information Sciences, vol. 290. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  10. Borrelli, F., Baotić, M., Bemporad, A., Morari, M.: An efficient algorithm for computing the state feedback optimal control law for discrete time hybrid systems. In: Proc. 2003 American Control Conference, Denver, Colorado, USA (June 2003)

    Google Scholar 

  11. Fukuda, K.: Cdd/cdd+ Reference Manual (December 1997), http://www.cs.mcgill.ca/~fukuda/soft/cdd_home/cdd.html

  12. Gilbert, E.G., Tin Tan, K.: Linear systems with state and control constraints: the theory and applications of maximal output admissible sets. IEEE Trans. Automatic Control 36(9), 1008–1020 (1991)

    Article  MATH  Google Scholar 

  13. Grieder, P., Borrelli, F., Torrisi, F.D., Morari, M.: Computation of the constrained infinite time linear quadratic regulator. In: Proc. 2003 American Control Conference, Denver, Colorado, USA (June 2003)

    Google Scholar 

  14. Grieder, P., Kvasnica, M., Baotić, M., Morari, M.: Low complexity control of piecewise affine systems with stability guarantee (2003) (submitted)

    Google Scholar 

  15. Grieder, P., Lüthi, M., Parillo, P., Morari, M.: Stability & feasibility of receding horizon control. In: European Control Conference, Cambridge, UK (September 2003)

    Google Scholar 

  16. Grieder, P., Morari, M.: Complexity reduction of receding horizon control. In: Proc. 42nd IEEE Conf. on Decision and Control, Maui, Hawaii, USA (December 2003)

    Google Scholar 

  17. Grieder, P., Parillo, P., Morari, M.: Robustness of receding horizon control. In: Proc. 42nd IEEE Conf. on Decision and Control, Maui, Hawaii, USA (December 2003)

    Google Scholar 

  18. Heemels, W.P.M.H., De Schutter, B., Bemporad, A.: Equivalence of hybrid dynamical models. Automatica 37(7), 1085–1091 (2001)

    Article  MATH  Google Scholar 

  19. ILOG, Inc. CPLEX 7.0 User Manual. Gentilly Cedex, France (2000)

    Google Scholar 

  20. Kerrigan, E.C., Maciejowski, J.M.: Robustly stable feedback min-max model predictive control. In: Proc. 2003 American Control Conference, Denver, Colorado, USA (June 2003)

    Google Scholar 

  21. Kerrigan, E.C., Mayne, D.Q.: Optimal control of constrained, piecewise affine systems with bounded disturbances. In: Proc. 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, USA (December 2002)

    Google Scholar 

  22. Kolmanovsky, I., Gilbert, E.G.: Theory and computation of disturbance invariant sets for discrete-time linear systems. Mathematical Problems in Egineering 4, 317–367 (1998)

    Article  MATH  Google Scholar 

  23. Löfberg, J.: Yalmip, http://www.control.isy.liu.se/~johanl/yalmip.html

  24. Mayne, D.Q., Raković, S.: Model predictive control of constrained piecewise affine discrete-time systems. Int. J. of Robust and Nonlinear Control 13(3), 261–279 (2003)

    Article  MATH  Google Scholar 

  25. Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.M.: Constrained model predictive control: Stability and optimality. Automatica 36(6), 789–814 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  26. Numerical Algorithms Group, Ltd. NAG Foundation Toolbox for MATLAB 6. Oxford, UK (2002)

    Google Scholar 

  27. Raković, S., Grieder, P., Kvasnica, M., Mayne, D.Q., Morari, M.: Computation of invariant sets for piecewise affine discrete time systems subject to bounded disturbances (2003) (submitted)

    Google Scholar 

  28. Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software, 625–653 (October 1999)

    Google Scholar 

  29. Tøndel, P., Johansen, T.A., Bemporad, A.: An algorithm for multi-parametric quadratic programming and explicit MPC solutions. In: Proc. 40th IEEE Conf. on Decision and Control (December 2001)

    Google Scholar 

  30. Veres, S.M.: Geometric Bounding Toolbox (GBT) for Matlab (2003)

    Google Scholar 

  31. Ziegler, G.M.: Lectures on Polytopes. Springer, Heidelberg (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kvasnica, M., Grieder, P., Baotić, M., Morari, M. (2004). Multi-Parametric Toolbox (MPT). In: Alur, R., Pappas, G.J. (eds) Hybrid Systems: Computation and Control. HSCC 2004. Lecture Notes in Computer Science, vol 2993. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24743-2_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24743-2_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21259-1

  • Online ISBN: 978-3-540-24743-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics