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Journal Articles Acta Applicandae Mathematicae Year : 2020

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.
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Dates and versions

hal-02280065 , version 1 (05-09-2019)
hal-02280065 , version 2 (16-09-2019)
hal-02280065 , version 3 (13-07-2020)

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Cite

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