### Abstract

Original language | English |
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Title of host publication | Proceedings of the 2012 American Control Conference |

Publication date | 2012 |

Pages | 295-300 |

ISBN (Print) | 978-1-4577-1094-0 |

Publication status | Published - 2012 |

Event | American Control Conference (ACC 2012) - Fairmont Queen Elizabeth, Montréal, Canada Duration: 27 Jun 2012 → 29 Jun 2012 http://a2c2.org/conferences/acc2012/index.php |

### Conference

Conference | American Control Conference (ACC 2012) |
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Location | Fairmont Queen Elizabeth |

Country | Canada |

City | Montréal |

Period | 27/06/2012 → 29/06/2012 |

Internet address |

Series | American Control Conference |
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ISSN | 0743-1619 |

### Bibliographical note

Paper number WeA08.6.### Cite this

*Proceedings of the 2012 American Control Conference*(pp. 295-300). American Control Conference

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*Proceedings of the 2012 American Control Conference.*American Control Conference, pp. 295-300, American Control Conference (ACC 2012), Montréal, Canada, 27/06/2012.

**Solution of Constrained Optimal Control Problems Using Multiple Shooting and ESDIRK Methods.** / Capolei, Andrea; Jørgensen, John Bagterp.

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

TY - GEN

T1 - Solution of Constrained Optimal Control Problems Using Multiple Shooting and ESDIRK Methods

AU - Capolei, Andrea

AU - Jørgensen, John Bagterp

N1 - Paper number WeA08.6.

PY - 2012

Y1 - 2012

N2 - In this paper, we describe a novel numerical algorithm for solution of constrained optimal control problems of the Bolza type for stiff and/or unstable systems. The numerical algorithm combines explicit singly diagonally implicit Runge-Kutta (ESDIRK) integration methods with a multiple shooting algorithm. As we consider stiff systems, implicit solvers with sensitivity computation capabilities for initial value problems must be used in the multiple shooting algorithm. Traditionally, multi-step methods based on the BDF algorithm have been used for such problems. The main novel contribution of this paper is the use of ESDIRK integration methods for solution of the initial value problems and the corresponding sensitivity equations arising in the multiple shooting algorithm. Compared to BDF-methods, ESDIRK-methods are advantageous in multiple shooting algorithms in which restarts and frequent discontinuities on each shooting interval are present. The ESDIRK methods are implemented using an inexact Newton method that reuses the factorization of the iteration matrix for the integration as well as the sensitivity computation. Numerical experiments are provided to demonstrate the algorithm.

AB - In this paper, we describe a novel numerical algorithm for solution of constrained optimal control problems of the Bolza type for stiff and/or unstable systems. The numerical algorithm combines explicit singly diagonally implicit Runge-Kutta (ESDIRK) integration methods with a multiple shooting algorithm. As we consider stiff systems, implicit solvers with sensitivity computation capabilities for initial value problems must be used in the multiple shooting algorithm. Traditionally, multi-step methods based on the BDF algorithm have been used for such problems. The main novel contribution of this paper is the use of ESDIRK integration methods for solution of the initial value problems and the corresponding sensitivity equations arising in the multiple shooting algorithm. Compared to BDF-methods, ESDIRK-methods are advantageous in multiple shooting algorithms in which restarts and frequent discontinuities on each shooting interval are present. The ESDIRK methods are implemented using an inexact Newton method that reuses the factorization of the iteration matrix for the integration as well as the sensitivity computation. Numerical experiments are provided to demonstrate the algorithm.

M3 - Article in proceedings

SN - 978-1-4577-1094-0

T3 - American Control Conference

SP - 295

EP - 300

BT - Proceedings of the 2012 American Control Conference

ER -