### Abstract

The optimal control of a spacecraft as it transitions between specified states using continuous thrust in a fixed amount of time is studied using a recently developed technique based on Hamilton-Jacobi theory. Starting from the 1st order necessary conditions for optimally, we derive a Hamiltonian system for the state and adjoints with split boundary conditions. Then, recognizing the two point boundary value problem as a canonical transformation, we employ generating functions to find the optimal feedback control as well as the optimal trajectory. Though we formulate the optimal control problem in the context of the necessary conditions for optimality, our closed-loop solution also formally satisfies the sufficient conditions for optimally via the fundamental connection between the optimal cost function and generating functions. A solution procedure for these generating functions is posed and numerically tested on a non-linear optimal rendezvous problem in the vicinity of a circular orbit. Generating functions are developed as series expansions, and the optimal trajectories obtained from them are compared favorably with those of a numerical solution to the two point boundary value problem using a forward shooting method.

Original language | English |
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Title of host publication | Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference 2005 |

Pages | 2332-2353 |

Number of pages | 22 |

Publication status | Published - 2005 Dec 1 |

Event | AIAA Guidance, Navigation, and Control Conference 2005 - San Francisco, CA, United States Duration: 2005 Aug 15 → 2005 Aug 18 |

### Publication series

Name | Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference |
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Volume | 3 |

### Other

Other | AIAA Guidance, Navigation, and Control Conference 2005 |
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Country | United States |

City | San Francisco, CA |

Period | 05/8/15 → 05/8/18 |

### All Science Journal Classification (ASJC) codes

- Engineering(all)

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## Cite this

*Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference 2005*(pp. 2332-2353). (Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference; Vol. 3).