### Abstract

This paper considers the optimal control problem for linear hybrid automata. In particular, it is shown that the problem can be transformed into a constrained optimization problem whose constraints are a set of inequalities with quantifiers. Quantifier Elimination (QE) techniques are employed in order to derive quantifier free inequalities that are linear. The optimal cost is obtained using linear programming. The optimal switching times and optimal continuous control inputs are computed and used in order to derive the optimal hybrid controller. Our results areapplied to an air traffic management example.

Original language | English |
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Number of pages | 6 |

Publication status | Published - Sep 2004 |

Event | Proceedings of the 7th IFAC International Workshop on Discrete Event Systems - Reims, France Duration: 22 Sep 2004 → 24 Sep 2004 |

### Conference

Conference | Proceedings of the 7th IFAC International Workshop on Discrete Event Systems |
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City | Reims, France |

Period | 22/09/04 → 24/09/04 |

### Keywords

- hybrid automata
- quantifier elimination
- time optimal control

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## Cite this

Pang, Y., & Spathopoulos, M. P. (2004).

*On weighted time optimal control for linear hybrid automata using quantifier elimination*. Paper presented at Proceedings of the 7th IFAC International Workshop on Discrete Event Systems, Reims, France, .