Title | Bounds on reachable sets using ordinary differential equations with linear programs embedded |

Publication Type | Journal Article |

Year of Publication | 2016 |

Authors | Harwood SM, Scott JK, Barton PI |

Journal | IMA Journal of Mathematical Control and Information |

Volume | 33 |

Issue | 2 |

Pagination | 519-541 |

Keywords | affine relaxations, reachable states, uncertain dynamic systems |

Abstract | This work considers the computation of rigorous componentwise time-varying bounds on the states of a non-linear control system. This work develops a new implementation of an existing bounding theory that exploits physical information to produce tight bounds. It is shown that the solution of a certain initial value problem in ordinary differential equations (ODEs) depending on parametric linear programs (LPs) (which are said to be ‘embedded’) yields componentwise bounds. To ensure the numerical tractability of such a formulation, some properties of the resulting system of ODEs with LPs embedded are discussed. Finally, the tightness of the bounds are demonstrated for models of reacting chemical systems with uncertain rate parameters. |

DOI | 10.1093/imamci/dnu054 |

# Bounds on reachable sets using ordinary differential equations with linear programs embedded

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