HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Journal articles

Tangency property and prior-saturation points in minimal time problems in the plane

Abstract : 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [28 references]  Display  Hide  Download

Contributor : Térence Bayen Connect in order to contact the contributor
Submitted on : Monday, July 13, 2020 - 4:03:07 PM
Last modification on : Wednesday, March 23, 2022 - 3:45:44 AM


Files produced by the author(s)



Térence Bayen, Olivier Cots. Tangency property and prior-saturation points in minimal time problems in the plane. Acta Applicandae Mathematicae, Springer Verlag, 2020, ⟨10.1007/s10440-020-00344-8⟩. ⟨hal-02280065v3⟩



Record views


Files downloads