Singularities of optimal time control-affine systems: the limit case
M. Orieux, R. Roussarie
TL;DR
This paper investigates the singularities in optimal time control problems for 4D control-affine systems with 2D controls, revealing the structure of the extremal flow and its stratification after regularization.
Contribution
It provides a detailed analysis of the bifurcation and singularities in 4D control-affine systems, demonstrating the smoothness and piece-wise smoothness of the extremal flow.
Findings
Extremal flow is smooth on a stratification.
The exponential map is piece-wise smooth.
Bifurcation analysis around nilpotent equilibrium.
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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Taxonomy
TopicsQuantum chaos and dynamical systems · Advanced Differential Equations and Dynamical Systems · Numerical methods for differential equations