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Min-Max Robust Control in LQ-Differential Games

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  • Jacob Engwerda

    (Retiree Tilburg University)

Abstract

In this paper, we consider the design of equilibrium linear feedback control policies in an uncertain process (e.g., an economy) affected by either one or more players. We consider a process which nominal (commonly believed) development in time is described by a linear system. Assuming every player is risk averse and has his own expectation about a worst-case development of the nominal process we model this problem using a linear quadratic differential game framework. Conditions under which equilibrium policies exist are studied. Assuming players have an infinite planning horizon, we provide a complete description in case the system is scalar, whereas for the multi-variable case, we provide existence results for some important classes of systems.

Suggested Citation

  • Jacob Engwerda, 2022. "Min-Max Robust Control in LQ-Differential Games," Dynamic Games and Applications, Springer, vol. 12(4), pages 1221-1279, December.
    • Handle: RePEc:spr:dyngam:v:12:y:2022:i:4:d:10.1007_s13235-021-00421-z
    DOI: 10.1007/s13235-021-00421-z
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    References listed on IDEAS

    as
    1. Jacob Engwerda, 2007. "Algorithms for computing Nash equilibria in deterministic LQ games," Computational Management Science, Springer, vol. 4(2), pages 113-140, April.
    2. Jacob Engwerda, 2017. "A Numerical Algorithm to Calculate the Unique Feedback Nash Equilibrium in a Large Scalar LQ Differential Game," Dynamic Games and Applications, Springer, vol. 7(4), pages 635-656, December.
    3. Alain Haurie & Jacek B Krawczyk & Georges Zaccour, 2012. "Games and Dynamic Games," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8442, February.
    4. Jacob Engwerda, 2017. "A Numerical Algorithm to Calculate the Unique Feedback Nash Equilibrium in a Large Scalar LQ Differential Game," Dynamic Games and Applications, Springer, vol. 7(4), pages 635-656, December.
    5. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, January.
    6. W. A. van den Broek & J. C. Engwerda & J. M. Schumacher, 2003. "Robust Equilibria in Indefinite Linear-Quadratic Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 565-595, December.
    7. W. A. van den Broek & J. C. Engwerda & J. M. Schumacher, 2003. "Robust Equilibria in Indefinite Linear-Quadratic Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 565-595, December.
    8. Valentijn Stienen & Jacob Engwerda, 2020. "Measuring Impact of Uncertainty in a Stylized Macroeconomic Climate Model within a Dynamic Game Perspective," Energies, MDPI, vol. 13(2), pages 1-39, January.
    9. Dockner Engelbert J. & Van Long Ngo, 1993. "International Pollution Control: Cooperative versus Noncooperative Strategies," Journal of Environmental Economics and Management, Elsevier, vol. 25(1), pages 13-29, July.
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    Cited by:

    1. Mikhail I. Krastanov & Rossen Rozenov & Boyan K. Stefanov, 2023. "On a Constrained Infinite-Time Horizon Linear Quadratic Game," Dynamic Games and Applications, Springer, vol. 13(3), pages 843-858, September.

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