Adjoint Equations
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
A system of first-order ordinary differential equations describing the time evolution of conjugate (adjoint) variables in optimal control theory, in the form lambda=-dH/dx. The adjoint equations, together with the state equations, form the canonical system that completely describes the optimal trajectory dynamics. The paper has seven adjoint equations corresponding to three velocity components, three position components, and mass. Solving the adjoint equations requires knowing the initial conjugate variable values, which are obtained by solving the two-point boundary value problem via the shooting method.
Application Value
A system of first-order ordinary differential equations describing the time evolution of conjugate (adjoint) variables in optimal control theory, in the form lambda=-dH/dx. The adjoint equations, together with the state equations, form the canonical system that completely describes the optimal trajectory dynamics. The paper has seven adjoint equations corresponding to three velocity components, three position components, and mass. Solving the adjoint equations requires knowing the initial conjugate variable values, which are obtained by solving the two-point boundary value problem via the shooting method.
Related Concepts
- Bivariate Gaussian Distribution
- Midcourse Impulse
- Zero-Thrust Reference Trajectory
- Co-state Variables
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