%0 Journal Article %T Tangency property and prior-saturation points in minimal time problems in the plane %+ EA2151 Laboratoire de Mathématiques d'Avignon (LMA) %+ Algorithmes Parallèles et Optimisation (IRIT-APO) %+ Institut National Polytechnique (Toulouse) (Toulouse INP) %A Bayen, Térence %A Cots, Olivier %< avec comité de lecture %@ 0167-8019 %J Acta Applicandae Mathematicae %I Springer Verlag %8 2020-06-29 %D 2020 %R 10.1007/s10440-020-00344-8 %K Geometric optimal control %K Singular arcs %K Minimum time problems %Z Mathematics [math] %Z Mathematics [math]/Optimization and Control [math.OC]Journal articles %X In this paper, we consider minimal time problems governed by control-affine-systems in the plane, and we focus on the synthesis problem in presence of a singular locus that involves a saturation point for the singular control. After giving sufficient conditions on the data ensuring occurence of a prior-saturation point and a switching curve, we show that the bridge, the optimal bang arc issued from the singular locus at this point) is tangent to the switching curve at the prior-saturation point. This property is proved using the Pontryagin Maximum Principle that also provides a set of non-linear equations that can be used to compute the prior-saturation point. These issues are illustrated on a fed-batch model in bioprocesses and on a Magnetic Resonance Imaging (MRI) model for which minimal time syntheses for the point-to-point problem are discussed. %G English %2 https://univ-avignon.hal.science/hal-02280065v3/document %2 https://univ-avignon.hal.science/hal-02280065v3/file/bayen_cots_review_2.pdf %L hal-02280065 %U https://univ-avignon.hal.science/hal-02280065 %~ UNIV-AVIGNON %~ UNIV-TLSE2 %~ UNIV-TLSE3 %~ CNRS %~ INSMI %~ SMS %~ UT1-CAPITOLE %~ TDS-MACS %~ LMA-UAPV %~ IRIT %~ IRIT-APO %~ IRIT-CISO %~ IRIT-INPT %~ TOULOUSE-INP %~ UNIV-UT3 %~ UT3-INP %~ UT3-TOULOUSEINP