### Abstract

Seeking the optimal control of spacecraft orbital maneuvers with non-smooth control logic in feedback sense, we extend our recently developed technique based on the Hamilton-Jacobi theory. Specifically we propose a new methodology stemming from the direct use of generating functions for solving optimal feedback control problem. Starting from the Hamilton-Jacobi equation for generating functions representing a two point boundary value problem, we derive a set of 1st order quasilinear partial differential equations with the associated initial condition, which forms the well-known Cauchy problem. These equations can also be derived by applying the invariant imbedding method to the two point boundary value problem. The solution to this Cauchy problem is utilized for determining the optimal control logic of spacecraft orbital maneuvers with hard and soft constraint boundary conditions. Illustrative examples demonstrate that this approach is, in contrast to the direct use of generating functions, promising for solving problems with non-smooth control logic usually caused by imposing control constraints.

Original language | English |
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Title of host publication | Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference 2006 |

Pages | 1764-1779 |

Number of pages | 16 |

Volume | 3 |

Publication status | Published - 2006 Dec 1 |

Event | AIAA Guidance, Navigation, and Control Conference 2006 - Keystone, CO, United States Duration: 2006 Aug 21 → 2006 Aug 24 |

### Other

Other | AIAA Guidance, Navigation, and Control Conference 2006 |
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Country | United States |

City | Keystone, CO |

Period | 06/8/21 → 06/8/24 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference 2006*(Vol. 3, pp. 1764-1779)

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*Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference 2006.*vol. 3, pp. 1764-1779, AIAA Guidance, Navigation, and Control Conference 2006, Keystone, CO, United States, 06/8/21.

**Optimal control of spacecraft orbital maneuvers by the Hamilton-Jacobi theory.** / Park, Chandeok; Scheeres, Daniel J.

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

TY - GEN

T1 - Optimal control of spacecraft orbital maneuvers by the Hamilton-Jacobi theory

AU - Park, Chandeok

AU - Scheeres, Daniel J.

PY - 2006/12/1

Y1 - 2006/12/1

N2 - Seeking the optimal control of spacecraft orbital maneuvers with non-smooth control logic in feedback sense, we extend our recently developed technique based on the Hamilton-Jacobi theory. Specifically we propose a new methodology stemming from the direct use of generating functions for solving optimal feedback control problem. Starting from the Hamilton-Jacobi equation for generating functions representing a two point boundary value problem, we derive a set of 1st order quasilinear partial differential equations with the associated initial condition, which forms the well-known Cauchy problem. These equations can also be derived by applying the invariant imbedding method to the two point boundary value problem. The solution to this Cauchy problem is utilized for determining the optimal control logic of spacecraft orbital maneuvers with hard and soft constraint boundary conditions. Illustrative examples demonstrate that this approach is, in contrast to the direct use of generating functions, promising for solving problems with non-smooth control logic usually caused by imposing control constraints.

AB - Seeking the optimal control of spacecraft orbital maneuvers with non-smooth control logic in feedback sense, we extend our recently developed technique based on the Hamilton-Jacobi theory. Specifically we propose a new methodology stemming from the direct use of generating functions for solving optimal feedback control problem. Starting from the Hamilton-Jacobi equation for generating functions representing a two point boundary value problem, we derive a set of 1st order quasilinear partial differential equations with the associated initial condition, which forms the well-known Cauchy problem. These equations can also be derived by applying the invariant imbedding method to the two point boundary value problem. The solution to this Cauchy problem is utilized for determining the optimal control logic of spacecraft orbital maneuvers with hard and soft constraint boundary conditions. Illustrative examples demonstrate that this approach is, in contrast to the direct use of generating functions, promising for solving problems with non-smooth control logic usually caused by imposing control constraints.

UR - http://www.scopus.com/inward/record.url?scp=33845790140&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845790140&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33845790140

SN - 1563478196

SN - 9781563478192

VL - 3

SP - 1764

EP - 1779

BT - Collection of Technical Papers - AIAA Guidance, Navigation, and Control Conference 2006

ER -