A PARAMETERIZED POLYHEDRA APPROACH FOR THE EXPLICIT ROBUST MODEL PREDICTIVE CONTROL

Sorin Olaru, Didier Dumur

Abstract

The paper considers the discrete-time linear time-invariant systems affected by input disturbances. The goal is to construct the robust model predictive control (RMPC) law taking into account the constraints existence from the design stage. The explicit formulation of the controller is found by exploiting the fact that the optimum of a min-max multi-parametric program is placed on the parameterized vertices of a parameterized polyhedron. As these vertices have specific validity domains, the control law has the form of a piecewise linear function of the current state. Its evaluation replaces the time-consuming on-line optimization problems.

References

  1. Bemporad, A., Borelli, F., and Morari, M. (2001). Robust model predictive control: Piecewise linear explicit solution. In Proc. European Control Conference.
  2. Bemporad, A., Fukuda, K., and Torrisi, F. (2002a). Convexity recognition of the union of polyhedra. In Computational Geometry, Vol. 18.
  3. Bemporad, A., Morari, M., Dua, V., and Pistikopoulos, E. (2002b). The explicit linear quadratic regulator for constrained systems. In Automatica, vol. 38.
  4. Borelli, F. (2003). Constrained Optimal Control of Linear and Hybrid Systems. Springer-Verlag, Berlin.
  5. Gal, T. and Nedoma, J. (1972). Multiparametric linear programming. In Management Science, 18.
  6. Goodwin, G., Seron, M., and Dona, J. D. (2004). Constrained Control and Estimation. Springer-Verlag, Berlin.
  7. Kerrigan, E. (2000). Robust Constraint Satisfaction: Invariant Sets and Predictive Control. PhD Thesis, University of Cambridge.
  8. Kerrigan, E. (2004). Feedback min-max model predictive control using a single linear program: Robust stability and the explicit solution. In International Journal of Robust and Nonlinear Control, vol.14.
  9. Kothare, M., Balakrishnan, V., and Morari, M. (1996). Robust constrained model predictive control using linear matrix inequalities. In Automatica, vol. 32.
  10. Leverge, H. (1994). A note on chernikova's algorithm. In Technical Report 635. IRISA, France.
  11. Loechner, V. and Wilde, D. (1997). Parameterized polyhedra and their vertices. In Int. Journal of Parallel Programming, vol. 25.
  12. Maciejowski, J. (2002). Predictive Control with Constraints. Prentice Hall, UK.
  13. Motzkin, T., Raiffa, H., Thompson, G., and Thrall, R. (1953). The double description method. In Theodore S. Motzkin: Selected Papers. Birkhauser, Boston.
  14. Olaru, S. and Dumur, D. (2004). A parameterized polyhedra approach for explicit constrained predictive control. In 43rd IEEE Conference on Decision and Control.
  15. Rossiter, J. (2003). Model-based Predictive Control. A practical approach. CRC Press.
  16. Schrijver, A. (1986). Theory of Linear and Integer Programming. John Wiley and Sons, NY.
  17. Scokaert, P. and Mayne, D. (1998). Min-max feedback model predictive control for constrained linear systems. In IEEE Trans. Automatic Control, 43.
  18. Seron, M., Goodwin, G., and Dona, J. D. (2002). Characterisation of receding horizon control for constrained linear systems. In Asian Journal of Control, vol. 5.
  19. Wilde, D. (1993). A library for doing polyhedral operations. In Technical report 785. IRISA, France.
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Paper Citation


in Harvard Style

Olaru S. and Dumur D. (2005). A PARAMETERIZED POLYHEDRA APPROACH FOR THE EXPLICIT ROBUST MODEL PREDICTIVE CONTROL . In Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO, ISBN 972-8865-31-7, pages 3-10. DOI: 10.5220/0001178400030010


in Bibtex Style

@conference{icinco05,
author={Sorin Olaru and Didier Dumur},
title={A PARAMETERIZED POLYHEDRA APPROACH FOR THE EXPLICIT ROBUST MODEL PREDICTIVE CONTROL},
booktitle={Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},
year={2005},
pages={3-10},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001178400030010},
isbn={972-8865-31-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,
TI - A PARAMETERIZED POLYHEDRA APPROACH FOR THE EXPLICIT ROBUST MODEL PREDICTIVE CONTROL
SN - 972-8865-31-7
AU - Olaru S.
AU - Dumur D.
PY - 2005
SP - 3
EP - 10
DO - 10.5220/0001178400030010