MODEL PREDICTIVE CONTROL FOR HYBRID SYSTEMS UNDER A STATE PARTITION BASED MLD APPROACH (SPMLD)

Jean Thomas, Didier Dumur, Jean Buisson, Herve Guéguen

2004

Abstract

This paper presents the State Partition based Mixed Logical Dynamical (SPMLD) formalism as a new modeling technique for a class of discrete-time hybrid systems, where the system is defined by different modes with continuous and logical control inputs and state variables, each model subject to linear constraints. The reformulation of the predictive strategy for hybrid systems under the SPMLD approach is then developed. This technique enables to considerably reduce the computation time (with respect to the classical MPC approaches for PWA and MLD models), as a positive feature for real time implementation. This strategy is applied in simulation to the control of a three tanks benchmark.

References

  1. Bemporad, A., 2003. “A Recursive Algorithm for Converting Mixed Logical Dynamical Systems into an Equivalent Piecewise Affine Form”, IEEE Trans. Autom. Contr.
  2. Bemporad, A., Ferrari-Trecate G., and Morari M., 2000. Observability and controllability of piecewise affine and hybrid systems. IEEE Trans. Automatic Control, 45(10):1864-1876.
  3. Bemporad, A., and Mignone, D., 2000.: Miqp.m: A Matlab function for solving mixed integer quadratic programs. Technical Report.
  4. Bemporad, A., Mignone, D. and Morari, M., 1999. Moving horizon estimation for hybrid systems and fault detection. In Proceedings of the American Control Conference, San Diego.
  5. Bemporad, A. and Morari, M., march 1999. Control of systems integrating logical, dynamics, and constraints. Automatica, 35(3):407-427.
  6. Branicky, M.S., Borkar, V.S. and Mitter, S.K., January 1998. A unified framework for hybrid control: model and optimal control theory. IEEE Transaction. on Automatic. Control, 43(1): 31-45.
  7. Dolanc, G., Juricic D., Rakar A., Petrovcic J. and Vrancic, D., 1998. Three-tank Benchmark Test. Technical Report Copernicus Project Report CT94-02337.
  8. Dumur, D. and Boucher, P.,1998. A Review Introduction to Linear GPC and Applications. Journal A, 39(4), pp. 21-35.
  9. Fletcher, R. and Leyffer, S., 1995. Numerical experience with lower bounds for MIQP branch and bound. Technical report, Dept. of Mathematics, University of Dundee, Scotland.
  10. Kerrigan, E., 2000. Robust Constraint Satisfaction: Invariant sets and predictive control. PhD thesis University of Cambridge.
  11. Pena, M.., Camacho, E. F. and Pinon, S., 2003. Hybrid systems for solving model predictive control of piecewise affine system. IFAC conference, Hybrid system analysis and design Saint Malo, France.
  12. Sontag, E.D., April 1981: Nonlinear regulation: the piecewise linear approach. IEEE Transaction. on Automatic. Control, 26(2):346-358.
  13. Torrisi, F., Bemporad, A. and Mignone, D., 2000. Hysdel - a tool for generating hybrid models. Technical report, AUT00-03, Automatic control laboratory, ETH Zuerich.
Download


Paper Citation


in Harvard Style

Thomas J., Dumur D., Buisson J. and Guéguen H. (2004). MODEL PREDICTIVE CONTROL FOR HYBRID SYSTEMS UNDER A STATE PARTITION BASED MLD APPROACH (SPMLD) . In Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO, ISBN 972-8865-12-0, pages 78-85. DOI: 10.5220/0001137000780085


in Bibtex Style

@conference{icinco04,
author={Jean Thomas and Didier Dumur and Jean Buisson and Herve Guéguen},
title={MODEL PREDICTIVE CONTROL FOR HYBRID SYSTEMS UNDER A STATE PARTITION BASED MLD APPROACH (SPMLD)},
booktitle={Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},
year={2004},
pages={78-85},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001137000780085},
isbn={972-8865-12-0},
}


in EndNote Style

TY - CONF
JO - Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,
TI - MODEL PREDICTIVE CONTROL FOR HYBRID SYSTEMS UNDER A STATE PARTITION BASED MLD APPROACH (SPMLD)
SN - 972-8865-12-0
AU - Thomas J.
AU - Dumur D.
AU - Buisson J.
AU - Guéguen H.
PY - 2004
SP - 78
EP - 85
DO - 10.5220/0001137000780085