### Abstract

This paper considers affine abstractions for over-approximating uncertain affine discrete-time systems, where the system uncertainties are represented by interval matrices, by a pair of affine functions in the sense of inclusion of all possible trajectories over the entire domain. The affine abstraction problem is a robust optimization problem with nonlinear uncertainties. To make this problem practically solvable, we convert the nonlinear uncertainties into linear uncertainties by exploiting the fact that the system uncertainties are hyperrectangles and thus, we only need to consider the vertices of the hyperrectangles instead of the entire uncertainty sets. Hence, affine abstraction can be solved efficiently by computing its corresponding robust counterpart to obtain a linear programming problem. Finally, we demonstrate the effectiveness of the proposed approach for abstracting uncertain driver intention models in an intersection crossing scenario.

Original language | English (US) |
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Title of host publication | 2019 American Control Conference, ACC 2019 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 2452-2457 |

Number of pages | 6 |

ISBN (Electronic) | 9781538679265 |

State | Published - Jul 1 2019 |

Event | 2019 American Control Conference, ACC 2019 - Philadelphia, United States Duration: Jul 10 2019 → Jul 12 2019 |

### Publication series

Name | Proceedings of the American Control Conference |
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Volume | 2019-July |

ISSN (Print) | 0743-1619 |

### Conference

Conference | 2019 American Control Conference, ACC 2019 |
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Country | United States |

City | Philadelphia |

Period | 7/10/19 → 7/12/19 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

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## Cite this

*2019 American Control Conference, ACC 2019*(pp. 2452-2457). [8815373] (Proceedings of the American Control Conference; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc..