%0 Journal Article %T Accessibility Properties of Abnormal Geodesics in Optimal Control Illustrated by Two Case Studies. %+ Mathematics for Control, Transport and Applications (McTAO) %+ Institut de Mathématiques de Bourgogne [Dijon] (IMB) %+ Laboratoire de Mathématiques de Bretagne Atlantique (LMBA) %+ Université Toulouse III - Paul Sabatier (UT3) %A Bonnard, Bernard %A Rouot, Jérémy %A Wembe, Boris %< avec comité de lecture %@ 2156-8472 %J Mathematical Control and Related Fields %I AIMS %8 2022-11 %D 2022 %R 10.3934/mcrf.2022052 %K Time minimal control for planar systems %K abnormal geodesics %K regularity of the value function %K Zermelo navigation problems %K Chemical reaction network %Z Mathematics [math]/Optimization and Control [math.OC]Journal articles %X In this article, we use two case studies from geometry and optimal control of chemical network to analyze the relation between abnormal geodesics in time optimal control, accessibility properties and regularity of the time minimal value function. %G English %2 https://inria.hal.science/hal-03310348v3/document %2 https://inria.hal.science/hal-03310348v3/file/zermelo_2022.pdf %L hal-03310348 %U https://inria.hal.science/hal-03310348