### Abstract

Motivated by a class of first order differential equations generated by some optimal control problems this paper provides, using the methodology introduced by the Theory of Connections, least-squares solutions of first-order differential equations systems subject to linear constraints on the vector’s components. This paper solves all different cases occurring in 2×2 linear time-varying systems with forcing term. Then, it shows how to solve a 4 × 4 system generated by a simple optimal control problem and how to solve a generic 3×3 time-varying differential equation system subject to relative and integral constraints on the vector components.

Original language | English (US) |
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Title of host publication | AAS/AIAA Astrodynamics Specialist Conference, 2018 |

Editors | Ryan M. Weisman, Puneet Singla, Belinda G. Marchand, Brandon A. Jones |

Publisher | Univelt Inc. |

Pages | 3041-3056 |

Number of pages | 16 |

ISBN (Print) | 9780877036579 |

State | Published - Jan 1 2018 |

Event | AAS/AIAA Astrodynamics Specialist Conference, 2018 - Montreal, Canada Duration: Aug 19 2018 → Aug 23 2018 |

### Publication series

Name | Advances in the Astronautical Sciences |
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Volume | 167 |

ISSN (Print) | 0065-3438 |

### Conference

Conference | AAS/AIAA Astrodynamics Specialist Conference, 2018 |
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Country | Canada |

City | Montreal |

Period | 8/19/18 → 8/23/18 |

### Fingerprint

### ASJC Scopus subject areas

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*AAS/AIAA Astrodynamics Specialist Conference, 2018*(pp. 3041-3056). (Advances in the Astronautical Sciences; Vol. 167). Univelt Inc..

**Theory of connections applied to first-order system of ordinary differential equations subject to component constraints.** / Mortari, Daniele; Furfaro, Roberto.

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

*AAS/AIAA Astrodynamics Specialist Conference, 2018.*Advances in the Astronautical Sciences, vol. 167, Univelt Inc., pp. 3041-3056, AAS/AIAA Astrodynamics Specialist Conference, 2018, Montreal, Canada, 8/19/18.

}

TY - GEN

T1 - Theory of connections applied to first-order system of ordinary differential equations subject to component constraints

AU - Mortari, Daniele

AU - Furfaro, Roberto

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Motivated by a class of first order differential equations generated by some optimal control problems this paper provides, using the methodology introduced by the Theory of Connections, least-squares solutions of first-order differential equations systems subject to linear constraints on the vector’s components. This paper solves all different cases occurring in 2×2 linear time-varying systems with forcing term. Then, it shows how to solve a 4 × 4 system generated by a simple optimal control problem and how to solve a generic 3×3 time-varying differential equation system subject to relative and integral constraints on the vector components.

AB - Motivated by a class of first order differential equations generated by some optimal control problems this paper provides, using the methodology introduced by the Theory of Connections, least-squares solutions of first-order differential equations systems subject to linear constraints on the vector’s components. This paper solves all different cases occurring in 2×2 linear time-varying systems with forcing term. Then, it shows how to solve a 4 × 4 system generated by a simple optimal control problem and how to solve a generic 3×3 time-varying differential equation system subject to relative and integral constraints on the vector components.

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UR - http://www.scopus.com/inward/citedby.url?scp=85063874170&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9780877036579

T3 - Advances in the Astronautical Sciences

SP - 3041

EP - 3056

BT - AAS/AIAA Astrodynamics Specialist Conference, 2018

A2 - Weisman, Ryan M.

A2 - Singla, Puneet

A2 - Marchand, Belinda G.

A2 - Jones, Brandon A.

PB - Univelt Inc.

ER -