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J. Preininger, T. Scarinci, V.M. Veliov:
"Metric regularity properties in bang-bang type linear-quadratic optimal control problems.";
Research Reports (Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics, Operations Research and Control Systems), 2017-07 (2017), 7; 26 pages.

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.

variational analysis, optimal control, linear control systems, bang-bang controls, metric regularity, stability analysis, Newton´s method

http://publik.tuwien.ac.at/files/publik_261882.pdf