### Abstract

In order to calculate the time history of the trajectory properties for an optimal continuous-thrust orbit transfer, the equations of motion and adjoint equations are integrated. For optimality, boundary conditions on the Hamiltonian must be satisfied, subject to meeting the initial and final values of the state vectors. At the beginning of the integration, the initial co-state variables for the adjoint equations are needed. However, the initial costate variables are usually unknown and thus it is necessary to find these variables. In this paper, evolutionary algorithms (EAs) are introduced and applied to find the values of the initial costate variables. Results obtained from the EAs are compared with the results previously published, and it was found that for several low Earth orbit to geostationary Earth orbit transfers, the initial values of the adjoints are comparable to those found using traditional optimization methods. While many traditional optimization methods are very sensitive to initial values of the adjoint variables, the EAs are able to find the initial values of the adjoints from lower and upper bounds that are up to ±25% away from the actual values.

Original language | English (US) |
---|---|

Title of host publication | Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference |

Pages | 667-688 |

Number of pages | 22 |

State | Published - Dec 1 2004 |

Event | Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference - Providence, RI, United States Duration: Aug 16 2004 → Aug 19 2004 |

### Publication series

Name | Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference |
---|---|

Volume | 2 |

### Other

Other | Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference |
---|---|

Country | United States |

City | Providence, RI |

Period | 8/16/04 → 8/19/04 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference*(pp. 667-688). [AIAA-2004-5085] (Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference; Vol. 2).

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*Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference.*, AIAA-2004-5085, Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference, vol. 2, pp. 667-688, Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference, Providence, RI, United States, 8/16/04.

**Optimal continuous thrust orbit transfer using evolutionary algorithms.** / Igarashi, Jugo; Spencer, David B.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Optimal continuous thrust orbit transfer using evolutionary algorithms

AU - Igarashi, Jugo

AU - Spencer, David B.

PY - 2004/12/1

Y1 - 2004/12/1

N2 - In order to calculate the time history of the trajectory properties for an optimal continuous-thrust orbit transfer, the equations of motion and adjoint equations are integrated. For optimality, boundary conditions on the Hamiltonian must be satisfied, subject to meeting the initial and final values of the state vectors. At the beginning of the integration, the initial co-state variables for the adjoint equations are needed. However, the initial costate variables are usually unknown and thus it is necessary to find these variables. In this paper, evolutionary algorithms (EAs) are introduced and applied to find the values of the initial costate variables. Results obtained from the EAs are compared with the results previously published, and it was found that for several low Earth orbit to geostationary Earth orbit transfers, the initial values of the adjoints are comparable to those found using traditional optimization methods. While many traditional optimization methods are very sensitive to initial values of the adjoint variables, the EAs are able to find the initial values of the adjoints from lower and upper bounds that are up to ±25% away from the actual values.

AB - In order to calculate the time history of the trajectory properties for an optimal continuous-thrust orbit transfer, the equations of motion and adjoint equations are integrated. For optimality, boundary conditions on the Hamiltonian must be satisfied, subject to meeting the initial and final values of the state vectors. At the beginning of the integration, the initial co-state variables for the adjoint equations are needed. However, the initial costate variables are usually unknown and thus it is necessary to find these variables. In this paper, evolutionary algorithms (EAs) are introduced and applied to find the values of the initial costate variables. Results obtained from the EAs are compared with the results previously published, and it was found that for several low Earth orbit to geostationary Earth orbit transfers, the initial values of the adjoints are comparable to those found using traditional optimization methods. While many traditional optimization methods are very sensitive to initial values of the adjoint variables, the EAs are able to find the initial values of the adjoints from lower and upper bounds that are up to ±25% away from the actual values.

UR - http://www.scopus.com/inward/record.url?scp=19644392803&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=19644392803&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:19644392803

SN - 1563477149

SN - 9781563477140

T3 - Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference

SP - 667

EP - 688

BT - Collection of Technical Papers - AIAA/AAS Astrodynamics Specialist Conference

ER -