### Abstract

The chapter introduces an approach to solve optimal control problems with multiple conflicting objectives. The approach proposed in this chapter generates sets of Pareto optimal control laws that satisfy a set of boundary conditions and path constraints. The chapter starts by introducing basic concepts of multi-objective optimisation and optimal control theory and then presents a general formulation of multi-objective optimal control problems in scalar form using the Pascoletti-Serafini scalarisation method. From this scalar form the chapter derives the first order necessary conditions for local optimality and develops a direct transcription method by Finite Elements in Time (DFET) that turns the infinite dimensional multi-objective optimal control problem into a finite dimensional multi-objective nonlinear programming problem (MONLP). The transcription method is proven to be locally convergent under some assumptions on the nature of the optimal control problem. A memetic agent-based optimisation approach is then proposed to solve the MONLP problem and return a partial reconstruction of the globally optimal Pareto set. An illustrative example concludes the chapter.

Original language | English |
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Title of host publication | Satellite Dynamics and Space Missions |

Editors | Giulio Baù, Alessandra Celletti, Cătălin Bogdan Galeş, Giovanni Federico Gronchi |

Place of Publication | Cham, Switzerland |

Publisher | Springer |

Pages | 257-289 |

Number of pages | 33 |

ISBN (Print) | 9783030206321, 9783030206338 |

DOIs | |

Publication status | Published - 19 Sep 2019 |

### Publication series

Name | Springer INdAM Series |
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Volume | 34 |

ISSN (Print) | 2281-518X |

ISSN (Electronic) | 2281-5198 |

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### Keywords

- finite elements
- multi-objective optimisation
- optimal control
- trajectory optimisation

### Cite this

*Satellite Dynamics and Space Missions*(pp. 257-289). (Springer INdAM Series; Vol. 34). Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-030-20633-8_6