Conjugate Point
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
A point along a reference extremal at which a nontrivial Jacobi field vanishes in its state component at both the initial time and this time. The absence of conjugate points on the open interval (0, tf] guarantees C0-local optimality of the extremal trajectory. This concept generalizes conjugacy from Riemannian geometry to the optimal control setting.
Application Value
共轭点 is verify局部optimal性 of core判据. 若参考极值曲线In 终端When 间之前无共轭点, 则该曲线In C0 拓扑下局部optimal. In optimalcontrolproblem of solve中, needinspect共轭点condition.
Related Concepts
- Orbital State Vector
- Coordinate Time
- Hill Frame
- Kepler's Laws
References
- Caillau et al. 2012 - Minimum fuel control of the planar circular restricted three-body problem
- Caillau and Daoud 2012, SIAM J. Control Optim. 50(6)