Transversality Conditions

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

Boundary conditions that conjugate variables must satisfy at the terminal time in an optimal control problem. The paper states the transversality conditions as lambda(tf)=(dPhi/dx)^T·v, where v is the Lagrange multiplier and Phi is the terminal constraint function. Transversality conditions link the terminal values of conjugate variables to terminal constraints, reflecting how state constraints at the terminal point affect the costates. When the terminal time is free, an additional condition that the Hamiltonian equals zero at the terminal time is also required.

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 该概念为地月空间任务设计提供了重要的理论基础 在实际工程中可用于轨道设计、任务规划或控制系统分析。

References

• 周净扬和周荻 - 2007 - 月球探测器软着陆精确建模及最优轨道设计