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Optimal Prioritized Infeasibility Handling in Model Predictive Control: Parametric Preemptive Multiobjective Linear Programming Approach

Author

Listed:
  • J. VADA

    (Energos)

  • O. SLUPPHAUG

    (ABB Industry)

  • T. A. JOHANSEN

    (Norwegian University of Science and Technology)

Abstract

All practical implementations of model-based predictive control (MPC) require a means to recover from infeasibility. We propose a strategy designed for linear state-space MPC with prioritized constraints. It relaxes optimally an infeasible MPC optimization problem into a feasible one by solving a single-objective linear program (LP) online in addition to the standard online MPC optimization problem at each sample. By optimal, it is meant that the violation of a lower prioritized constraint cannot be made less without increasing the violation of a higher prioritized constraint. The problem of computing optimal constraint violations is naturally formulated as a parametric preemptive multiobjective LP. By extending well-known results from parametric LP, the preemptive multiobjective LP is reformulated into an equivalent standard single-objective LP. An efficient algorithm for offline design of this LP is given, and the algorithm is illustrated on an example.

Suggested Citation

  • J. Vada & O. Slupphaug & T. A. Johansen, 2001. "Optimal Prioritized Infeasibility Handling in Model Predictive Control: Parametric Preemptive Multiobjective Linear Programming Approach," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 385-413, May.
    • Handle: RePEc:spr:joptap:v:109:y:2001:i:2:d:10.1023_a:1017570507125
    DOI: 10.1023/A:1017570507125
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    Cited by:

    1. M. Zarepisheh & E. Khorram, 2011. "On the transformation of lexicographic nonlinear multiobjective programs to single objective programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(2), pages 217-231, October.

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