Singularities of optimal time control-affine systems: the limit case

2019/07/05 by Orieux, M., Roussarie, R.
#Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1907.02931

Abstract

We study the singularities for minimum time control-affine problems in 4D with 2D controls. After regularization, the problem boils down to the study of a bifurcation around some nilpotent equilibrium in the singular locus. We show that the extremal flow - thus, the exponential map - is smooth on a stratification, and therefore piece-wise smooth.

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