### Abstract

In this paper, the problem of synthesizing a hybrid controller for a specification expressed as a temporal logic formula ø is considered. We propose a hierarchical approach which consists of three steps. First, the plant to be controlled is abstracted to a fully actuated system. Using the notion of approximate simulation relation, we design a continuous interface allowing the plant to track the trajectories of its abstraction with a guaranteed precision δ. The second step, which is also the main contribution of this paper, consists in deriving a more robust specification ø from the temporal logic formula ø such that given a trajectory satisfying ø′ any other trajectory remaining within distance S satisfies ø. Third, we design a hybrid controller for the abstraction such that all its trajectories satisfy the robust specification ø′. Then, the trajectories of the plant satisfy the original specification. An application to the control of a second order model of a planar robot in a polygonal environment is considered.

Original language | English (US) |
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Title of host publication | Hybrid Systems |

Subtitle of host publication | Computation and Control - 10th International Conference, HSCC 2007, Proceedings |

Publisher | Springer Verlag |

Pages | 203-216 |

Number of pages | 14 |

ISBN (Print) | 9783540714927 |

State | Published - Jan 1 2007 |

Externally published | Yes |

Event | 10th International Conference on Hybrid Systems: Computation and Control, HSCC 2007 - Pisa, Italy Duration: Apr 3 2007 → Apr 5 2007 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4416 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 10th International Conference on Hybrid Systems: Computation and Control, HSCC 2007 |
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Country | Italy |

City | Pisa |

Period | 4/3/07 → 4/5/07 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Hybrid Systems: Computation and Control - 10th International Conference, HSCC 2007, Proceedings*(pp. 203-216). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4416 LNCS). Springer Verlag.