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Preininger, J., Scarinci, T., & Veliov, V. M. (2018). Metric regularity properties in bang-bang type linear-quadratic optimal control problems. Set-Valued and Variational Analysis, 27(2), 381–404. https://doi.org/10.1007/s11228-018-0488-1
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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Journal:
Set-Valued and Variational Analysis
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ISSN:
1877-0533
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Date (published):
2018
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Number of Pages:
24
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Peer reviewed:
Yes
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Keywords:
Applied Mathematics; Analysis; Numerical Analysis; stability analysis; optimal control; linear control systems; metric regularity; Geometry and Topology; Statistics and Probability; variational analysis; bang-bang controls; Newton´s method
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Abstract:
The paper investigates the Lipschitz/Hölder stability with respect to perturbations of the solutions of linear-quadratic optimal control problems where the control variable appears linearly and the optimal one is of bang-bang type. Conditions for bi-metric regularity and (Hölder) metric sub-regularity are established, involving only the order of the zeros of the associated switching function and smoothness of the data. The results provide a basis for investigation of various approximation methods and are applied in this paper for convergence analysis of a Newton-type method.
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Research Areas:
Fundamental Mathematics Research: 40% Modelling and Simulation: 60%
