[Back]

N. Osmolovskii, V.M. Veliov:
"Metric sub-regularity in optimal control of affine problems with free end state";
ESAIM: Control Optimisation And Calculus Of Variations, 26 (2020), 47; 19 pages.

The paper investigates the property of Strong Metric sub-Regularity (SMsR) of the mappingrepresenting the first order optimality system for a Lagrange-type optimal control problem whichis affine with respect to the control. The terminal time is fixed, the terminal state is free, and thecontrol values are restricted in a convex compact setU. The SMsR property is associated with areference solution of the optimality system and ensures that small additive perturbations in thesystem result in solutions which are at distance to the reference one, at most proportional to thesize of the perturbations. A general sufficient condition for SMsR is obtained for appropriatespace settings and then specialized in the case of a polyhedral setUand purely bang-bangreference control. Sufficient second-order optimality conditions are obtained as a by-product ofthe analysis. Finally, the obtained results are utilized for error analysis of the Euler discretizationscheme applied to affine problems.

optimal control, affine control problems, bang-bang control, metric regularity, Pon-tryagin´s maximum principle, second-order optimality conditions, Euler discretization

http://dx.doi.org/10.1051/cocv/2019046