Preininger, J., Scarinci, T., & Veliov, V. M. (2017). Metric regularity properties in bang-bang type linear-quadratic optimal control problems. (No. 2017–07). Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics, Operations Research and Control Systems. http://hdl.handle.net/20.500.12708/146874
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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Series:
ORCOS (Operations Research and Control Systems Theory)
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Report No.:
2017-07
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Date (published):
2017
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Number of Pages:
24
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Publisher:
Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics, Operations Research and Control Systems
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Publisher:
Vienna, Austria
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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
en
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.
