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Relaxed dissipativity assumptions and a simplified algorithm for multiobjective MPC

Author

Listed:
  • Gabriele Eichfelder

    (Technische Universität Ilmenau)

  • Lars Grüne

    (Universität Bayreuth)

  • Lisa Krügel

    (Universität Bayreuth)

  • Jonas Schießl

    (Universität Bayreuth)

Abstract

We consider nonlinear model predictive control (MPC) with multiple competing cost functions. In each step of the scheme, a multiobjective optimal control problem with a nonlinear system and terminal conditions is solved. We propose an algorithm and give performance guarantees for the resulting MPC closed loop system. Thereby, we significantly simplify the assumptions made in the literature so far by assuming strict dissipativity and the existence of a compatible terminal cost for one of the competing objective functions only. We give conditions which ensure asymptotic stability of the closed loop and, what is more, obtain performance estimates for all cost criteria. Numerical simulations on various instances illustrate our findings. The proposed algorithm requires the selection of an efficient solution in each iteration, thus we examine several selection rules and their impact on the results. and we also examine numerically how different selection rules impact the results

Suggested Citation

  • Gabriele Eichfelder & Lars Grüne & Lisa Krügel & Jonas Schießl, 2023. "Relaxed dissipativity assumptions and a simplified algorithm for multiobjective MPC," Computational Optimization and Applications, Springer, vol. 86(3), pages 1081-1116, December.
    • Handle: RePEc:spr:coopap:v:86:y:2023:i:3:d:10.1007_s10589-022-00398-4
    DOI: 10.1007/s10589-022-00398-4
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    References listed on IDEAS

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    1. Stefan Banholzer & Giulia Fabrini & Lars Grüne & Stefan Volkwein, 2020. "Multiobjective Model Predictive Control of a Parabolic Advection-Diffusion-Reaction Equation," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    2. William A. Brock & Leonard J. Mirman, 2001. "Optimal Economic Growth And Uncertainty: The Discounted Case," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 1, pages 3-37, Edward Elgar Publishing.
    3. Matthias Ehrgott, 2005. "Multicriteria Optimization," Springer Books, Springer, edition 0, number 978-3-540-27659-3, March.
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    Cited by:

    1. Helmut Maurer & Willi Semmler, 2025. "Multi-objective optimal control with carbon emission and temperature constraints: for achieving a low-fossil-fuel economy," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 33(2), pages 449-471, June.

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