Logarithmic Barrier Homotopy

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A homotopy continuation method for bang-bang optimal control that adds logarithmic barrier terms to the cost functional, excluding both zero and saturated control values (0<|u|<1). This ensures the maximized Hamiltonian is smooth, enabling differential continuation and second-order optimality tests. The barrier parameter epsilon is gradually reduced to recover the original minimum-fuel problem.

Application Value

为航天器的精确控制提供理论依据，确保任务执行的可靠性 用于评估导航系统的精度上限，指导滤波器设计。

References

• Caillau et al. 2012 - Minimum fuel control of the planar circular restricted three-body problem