### Abstract

Partial (or block) condensing is a recently proposed technique to reformulate a Model Predictive Control (MPC) problem into a form more suitable for structure-exploiting Quadratic Programming (QP) solvers. It trades off horizon length for input vector size, and this degree of freedom can be employed to find the best problem size for the QP solver at hand. This paper proposes a Hessian condensing algorithm particularly well suited for partial condensing, where a state component is retained as an optimization variable at each stage of the partially condensed MPC problem. The optimal input-horizon trade-off is investigated from a theoretical point of view (based on algorithms flop count) as well as by benchmarking (in practice, the performance of linear algebra routines for different matrix sizes plays a key role). Partial condensing can also be seen as a technique to replace many operations on small matrices with fewer operations on larger matrices, where linear algebra routines perform better. Therefore, in case of small-scale MPC problems, partial condensing can greatly improve performance beyond the flop count reduction.

Original language | English |
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Title of host publication | Proceedings of the 55th IEEE Conference on Decision and Control (CDC 2016) |

Publisher | IEEE |

Publication date | 2016 |

Pages | 4457-4462 |

ISBN (Print) | 978-1-5090-1836-9 |

DOIs | |

Publication status | Published - 2016 |

Event | 55th IEEE Conference on Decision and Control - Las Vegas, United States Duration: 12 Dec 2016 → 14 Dec 2016 Conference number: 55 http://cdc2016.ieeecss.org/index.php |

### Conference

Conference | 55th IEEE Conference on Decision and Control |
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Number | 55 |

Country | United States |

City | Las Vegas |

Period | 12/12/2016 → 14/12/2016 |

Internet address |

## Cite this

Frison, G., Kouzoupis, D., Jørgensen, J. B., & Diehl, M. (2016). An Efficient Implementation of Partial Condensing for Nonlinear Model Predictive Control. In

*Proceedings of the 55th IEEE Conference on Decision and Control (CDC 2016)*(pp. 4457-4462). IEEE. https://doi.org/10.1109/CDC.2016.7798946