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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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Submitted on : Monday, July 13, 2020 - 4:03:07 PM
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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⟩

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