Pontryagin Optimality Conditions

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A set of necessary conditions derived from the Pontryagin Maximum Principle, including the optimal control law (analytical expressions for thrust direction and magnitude), costate differential equations, and transversality conditions. Indirect methods require all conditions to be satisfied simultaneously.

Application Value

The Pontryagin Optimality Conditions plays a significant role in cislunar space mission design, analysis, and control. In orbital design, it can be leveraged for transfer trajectory optimization; in navigation and control, it improves mission execution precision and reliability; in system analysis, it facilitates deeper understanding of complex multi-body dynamical behavior, guiding mission planning and risk assessment.

References

  • Oshima et al. 2017
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Contributors: ouyangjiahong, Ou Yang Jiahong