External Ellipsoidal Approximations for Set Evolution Equations

Steven Duda (), Edeltraud Gehrig () and Thomas Lorenz ()
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Steven Duda: RheinMain University of Applied Sciences
Edeltraud Gehrig: RheinMain University of Applied Sciences
Thomas Lorenz: RheinMain University of Applied Sciences

Journal of Optimization Theory and Applications, 2022, vol. 192, issue 3, No 1, 759-798

Abstract: 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.

Keywords: Set differential equations; Morphological equations; Reachable sets; Integral funnel; Ellipsoidal approximations; Guaranteed state estimation; 34A60; 34G25; 49J53; 93B03; 93C41 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-021-01984-y

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