Dominguez Corella, A., & Veliov, V. (2022). Hölder Regularity in Bang-Bang Type Affine Optimal Control Problems. In Large-Scale Scientific Computing 3th International Conference, LSSC 2021 (pp. 306–313). Springer. https://doi.org/10.1007/978-3-030-97549-4_35
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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Published in:
Large-Scale Scientific Computing 3th International Conference, LSSC 2021
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Date (published):
18-Mar-2022
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Event name:
13th International Conference, LSSC 2021
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Event date:
7-Jun-2021 - 11-Jun-2021
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Event place:
Sozopol, Bulgaria
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Number of Pages:
8
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Publisher:
Springer, Schweiz
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Peer reviewed:
Yes
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Keywords:
Affine problems; Hölder metric sub-regularity; Optimal control
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Abstract:
This paper revisits the issue of Hölder Strong Metric sub-Regularity (HSMs-R) of the optimality system associated with ODE optimal control problems that are affine with respect to the control. The main contributions are as follows. First, the metric in the control space, introduced in this paper, differs from the ones used so far in the literature in that it allows to take into consideration the bang-bang structure of the optimal control functions. This is especially important in the analysis of Model Predictive Control algorithms. Second, the obtained sufficient conditions for HSMs-R extend the known ones in a way which makes them applicable to some problems which are non-linear in the state variable and the Hölder exponent is smaller than one (that is, the regularity is not Lipschitz).
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Project title:
Optimale Steuerung mit endlichen Steuerungsmengen und Anwendungen in der Modelbasierten Regelung: P 31400-N32 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
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Research Areas:
Mathematical and Algorithmic Foundations: 20% Fundamental Mathematics Research: 80%
