Abnormal Extremal
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
An extremal in the Pontryagin maximum principle for which the cost multiplier p0 equals zero. The cost functional then vanishes from the Hamiltonian, and the optimal control is determined solely by the dynamics. For minimum-fuel problems, abnormal extremals provably do not exist when the transfer time strictly exceeds the minimum time.
Application Value
An extremal in the Pontryagin maximum principle for which the cost multiplier p0 equals zero. The cost functional then vanishes from the Hamiltonian, and the optimal control is determined solely by the dynamics. For minimum-fuel problems, abnormal extremals provably do not exist when the transfer time strictly exceeds the minimum time.
Related Concepts
- Time-Varying System
- Lipschitz Condition
- Variable-Time Targeting
- Return Corridor
References
- Caillau et al. 2012 - Minimum fuel control of the planar circular restricted three-body problem