About the prior-saturation phenomenon for minimal time problems in the plane

Térence Bayen (1) , Olivier Cots (2, 3)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 IRIT-APO - Algorithmes Parallèles et Optimisation
3 Toulouse INP - Institut National Polytechnique (Toulouse)

We consider minimal time problems governed by control-affine-systems in the plane. We focus on the synthesis problem in presence of a singular locus that involves a saturation point for the singular control. We show that the minimum time synthesis can exhibit a prior-saturation point at the intersection of the singular locus and a switching curve. We also provide a set of non-linear equations to compute the prior-saturation point, and, at this point, we show a tangency property involving the switching curve.

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Térence Bayen, Olivier Cots. About the prior-saturation phenomenon for minimal time problems in the plane. 2019. ⟨hal-02070271⟩