### Abstract

This paper proposes a new method of optimal trajectory design for formation flying along an elliptical orbit. Under linearized assumptions and a quadratic performance index, the optimal cost is quadratic in the initial state. Attractive sets of optimal control are defined as contours of the optimal cost based on linear quadratic regulator theory. It describes a set of all initial states to reach a desired state by a given cost. By solving the optimal control problem for TH equations, the optimal cost is obtained as a time-periodic function. This paper develops the attractive set for a time-periodic system and procedure to draw the attractive set is shown. The advantage of using attractive sets for optimal trajectory design is that it can determine the optimal initial state immediately. The various shape of the periodic orbit and the attractive sets are demonstrated by weight parameters of optimal control theory.

Original language | English |
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Title of host publication | 68th International Astronautical Congress, IAC 2017 |

Subtitle of host publication | Unlocking Imagination, Fostering Innovation and Strengthening Security |

Publisher | International Astronautical Federation, IAF |

Pages | 7186-7194 |

Number of pages | 9 |

ISBN (Print) | 9781510855373 |

Publication status | Published - Jan 1 2017 |

Event | 68th International Astronautical Congress: Unlocking Imagination, Fostering Innovation and Strengthening Security, IAC 2017 - Adelaide, Australia Duration: Sep 25 2017 → Sep 29 2017 |

### Publication series

Name | Proceedings of the International Astronautical Congress, IAC |
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Volume | 11 |

ISSN (Print) | 0074-1795 |

### Other

Other | 68th International Astronautical Congress: Unlocking Imagination, Fostering Innovation and Strengthening Security, IAC 2017 |
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Country | Australia |

City | Adelaide |

Period | 9/25/17 → 9/29/17 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*68th International Astronautical Congress, IAC 2017: Unlocking Imagination, Fostering Innovation and Strengthening Security*(pp. 7186-7194). (Proceedings of the International Astronautical Congress, IAC; Vol. 11). International Astronautical Federation, IAF.

**Formation flying along elliptical orbit using attractive sets of optimal control.** / Yamane, Motoki; Bando, Mai; Hokamoto, Shinji.

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

*68th International Astronautical Congress, IAC 2017: Unlocking Imagination, Fostering Innovation and Strengthening Security.*Proceedings of the International Astronautical Congress, IAC, vol. 11, International Astronautical Federation, IAF, pp. 7186-7194, 68th International Astronautical Congress: Unlocking Imagination, Fostering Innovation and Strengthening Security, IAC 2017, Adelaide, Australia, 9/25/17.

}

TY - GEN

T1 - Formation flying along elliptical orbit using attractive sets of optimal control

AU - Yamane, Motoki

AU - Bando, Mai

AU - Hokamoto, Shinji

PY - 2017/1/1

Y1 - 2017/1/1

N2 - This paper proposes a new method of optimal trajectory design for formation flying along an elliptical orbit. Under linearized assumptions and a quadratic performance index, the optimal cost is quadratic in the initial state. Attractive sets of optimal control are defined as contours of the optimal cost based on linear quadratic regulator theory. It describes a set of all initial states to reach a desired state by a given cost. By solving the optimal control problem for TH equations, the optimal cost is obtained as a time-periodic function. This paper develops the attractive set for a time-periodic system and procedure to draw the attractive set is shown. The advantage of using attractive sets for optimal trajectory design is that it can determine the optimal initial state immediately. The various shape of the periodic orbit and the attractive sets are demonstrated by weight parameters of optimal control theory.

AB - This paper proposes a new method of optimal trajectory design for formation flying along an elliptical orbit. Under linearized assumptions and a quadratic performance index, the optimal cost is quadratic in the initial state. Attractive sets of optimal control are defined as contours of the optimal cost based on linear quadratic regulator theory. It describes a set of all initial states to reach a desired state by a given cost. By solving the optimal control problem for TH equations, the optimal cost is obtained as a time-periodic function. This paper develops the attractive set for a time-periodic system and procedure to draw the attractive set is shown. The advantage of using attractive sets for optimal trajectory design is that it can determine the optimal initial state immediately. The various shape of the periodic orbit and the attractive sets are demonstrated by weight parameters of optimal control theory.

UR - http://www.scopus.com/inward/record.url?scp=85051445928&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85051445928&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85051445928

SN - 9781510855373

T3 - Proceedings of the International Astronautical Congress, IAC

SP - 7186

EP - 7194

BT - 68th International Astronautical Congress, IAC 2017

PB - International Astronautical Federation, IAF

ER -