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A. Corella, V.M. Veliov:
"Hölder Regularity in Bang-Bang Type Affine Optimal Control Problems.";
Research Reports (Vienna University of Technology, Institute of Statistics and Mathematical Methods in Economics, Operations Research and Control Systems), 2021-03 (2021), 03; 10 pages.

This paper revisits the issue of H ̈older 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 H ̈older exponent is smaller than one (that is, the regularity is not Lipschitz).

optimal control, affine problems, Hölder metric sub-regularity

https://publik.tuwien.ac.at/files/publik_298640.pdf