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External Ellipsoidal Approximations for Set Evolution Equations

Author

Listed:
  • Steven Duda

    (RheinMain University of Applied Sciences)

  • Edeltraud Gehrig

    (RheinMain University of Applied Sciences)

  • Thomas Lorenz

    (RheinMain University of Applied Sciences)

Abstract

In many applications, uncertainty and imprecision in control systems require the focus on reachable sets instead of single state vectors. Then, closed-loop controls also refer to these attainable sets leading to a class of set evolution problems. We suggest sufficient conditions for its well-posedness and for approximating their solutions by intersections of finitely many time-dependent ellipsoids characterized by solutions to a system of ordinary differential equations.

Suggested Citation

  • Steven Duda & Edeltraud Gehrig & Thomas Lorenz, 2022. "External Ellipsoidal Approximations for Set Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 759-798, March.
    • Handle: RePEc:spr:joptap:v:192:y:2022:i:3:d:10.1007_s10957-021-01984-y
    DOI: 10.1007/s10957-021-01984-y
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    References listed on IDEAS

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    1. F. L. Chernousko, 2010. "Optimal Ellipsoidal Estimates of Uncertain Systems: An Overview and New Results," Lecture Notes in Economics and Mathematical Systems, in: Kurt Marti & Yuri Ermoliev & Marek Makowski (ed.), Coping with Uncertainty, chapter 0, pages 141-161, Springer.
    2. A. B. Kurzhanski & P. Varaiya, 2011. "Optimization of Output Feedback Control Under Set-Membership Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 11-32, October.
    3. F. L. Chernousko & D. Ya. Rokityanskii, 2000. "Ellipsoidal Bounds on Reachable Sets of Dynamical Systems with Matrices Subjected to Uncertain Perturbations1," Journal of Optimization Theory and Applications, Springer, vol. 104(1), pages 1-19, January.
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