Accessibility Properties of Abnormal Geodesics in Optimal Control Illustrated by Two Case Studies

TL;DR

This paper investigates the accessibility properties of abnormal geodesics in optimal control, using two case studies from geometry and chemical network control to explore their impact on the regularity of the minimal time function.

Contribution

It introduces a detailed analysis of abnormal geodesics in optimal control and their influence on the regularity of the value function through two illustrative case studies.

Findings

Abnormal geodesics significantly affect the regularity of the minimal time function.

Case studies demonstrate the relationship between abnormal geodesics and accessibility properties.

Insights contribute to understanding control system behaviors in geometry and chemical networks.

Abstract

In this article, we use two case studies from geometry and optimal control of chemical network to analyze the relation between abnormal geodesics in time optimal control, accessibility properties and regularity of the time minimal value function.