Singular Arc

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A segment of the extremal flow where the switching function vanishes identically. In this case the control does not take boundary values but is given by the singular control formula. Singular arcs arise in connection with the non-involutivity of the distribution and Goh's second-order necessary condition.

Application Value

This concept is essential for understanding motion characteristics in orbital design and control, and plays a vital role in mission success.

Related Concepts

• Minimum Norm Solution
• Rigid Body Dynamics
• Variable-Size Design Space, VSDS
• Analytical Gradient

References

• You and Dai, 2022, JGCD, doi:10.2514/1.G006815
• Caillau and Daoud 2012, SIAM J. Control Optim. 50(6)