Tangency property and prior-saturation points in planar minimal time problems

Abstract

In this paper, we address properties of the minimal time synthesis for control-affine-systems in the plane involving a saturation point for the singular control. First, we provide sufficient conditions on the data ensuring occurence of a prior-saturation point. Then, we show that the bridge (i.e., the optimal bang arc issued from the singular locus at this point) is tangent to the switching curve at the prior-saturation point. We illustrate these results on a fed-batch model in bioprocesses.