Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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 :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [31 references]  Display  Hide  Download
Contributor : Terence Bayen Connect in order to contact the contributor
Submitted on : Thursday, September 5, 2019 - 10:03:56 PM
Last modification on : Wednesday, June 9, 2021 - 10:00:13 AM
Long-term archiving on: : Thursday, February 6, 2020 - 3:30:27 AM


Files produced by the author(s)


  • HAL Id : hal-02280065, version 1


Térence Bayen, Olivier Cots. Tangency property and prior-saturation points in minimal time problems in the plane. 2019. ⟨hal-02280065v1⟩



Record views


Files downloads