Structural stability of bang-bang trajectories with a double switching time in the minimum time problem

TL;DR

This paper investigates the robustness of optimal bang-bang control trajectories with a double switch in minimum time problems, focusing on their structural stability under perturbations.

Contribution

It provides a novel analysis of the structural stability of bang-bang trajectories with double switches in minimum time optimal control problems.

Findings

Double switch trajectories exhibit specific stability properties.

Structural stability depends on the nature of the double switch.

Results inform robustness analysis of time-optimal control solutions.

Abstract

In this paper we consider the problem of structural stability of strong local optimisers for the minimum time problem in the case when the nominal problem has a bang-bang strongly local optimal control which exhibits a double switch.