@article{LANOTTE20071575,
    Abstract = {We propose a new approximation technique for Hybrid Automata. Given any Hybrid Automaton H, we call Approx(H,k) the Polynomial Hybrid Automaton obtained by approximating each formula ϕ in H with the formulae ϕk obtained by replacing the functions in ϕ with their Taylor polynomial of degree k. We prove that Approx(H,k) is an over-approximation of H. We study the conditions ensuring that, given any ϵ>0, some k0 exists such that, for all k>k0, the ``distance'' between any vector satisfying ϕk and at least one vector satisfying ϕ is less than ϵ. We study also conditions ensuring that, given any ϵ>0, some k0 exists such that, for all k>k0, the ``distance'' between any configuration reached by Approx(H,k) in n steps and at least one configuration reached by H in n steps is less than ϵ.},
    Author = {Lanotte, Ruggero and Tini, Simone},
    File = {Taylor approximation for hybrid systems - 1-s2.0-S0890540107000739-main - z.pdf},
    ISSN = {0890-5401},
    Journal = {Information and Computation},
    Number = {11},
    Pages = {1575-1607},
    Title = {Taylor approximation for hybrid systems},
    URL = {https://www.sciencedirect.com/science/article/pii/S0890540107000739},
    Volume = {205},
    Year = {2007},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0890540107000739},
    bdsk-url-2 = {https://doi.org/10.1016/j.ic.2007.05.004},
    date-added = {2021-04-29 11:08:28 +0200},
    date-modified = {2021-04-29 11:08:28 +0200},
    doi = {10.1016/j.ic.2007.05.004}
}

@article{LANOTTE20071575, Abstract = {We propose a new approximation technique for Hybrid Automata. Given any Hybrid Automaton H, we call Approx(H,k) the Polynomial Hybrid Automaton obtained by approximating each formula ϕ in H with the formulae ϕk obtained by replacing the functions in ϕ with their Taylor polynomial of degree k. We prove that Approx(H,k) is an over-approximation of H. We study the conditions ensuring that, given any ϵ>0, some k0 exists such that, for all k>k0, the distance'' between any vector satisfying ϕk and at least one vector satisfying ϕ is less than ϵ. We study also conditions ensuring that, given any ϵ>0, some k0 exists such that, for all k>k0, thedistance'' between any configuration reached by Approx(H,k) in n steps and at least one configuration reached by H in n steps is less than ϵ.}, Author = {Lanotte, Ruggero and Tini, Simone}, File = {Taylor approximation for hybrid systems - 1-s2.0-S0890540107000739-main - z.pdf}, ISSN = {0890-5401}, Journal = {Information and Computation}, Number = {11}, Pages = {1575-1607}, Title = {Taylor approximation for hybrid systems}, URL = {https://www.sciencedirect.com/science/article/pii/S0890540107000739}, Volume = {205}, Year = {2007}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0890540107000739}, bdsk-url-2 = {https://doi.org/10.1016/j.ic.2007.05.004}, date-added = {2021-04-29 11:08:28 +0200}, date-modified = {2021-04-29 11:08:28 +0200}, doi = {10.1016/j.ic.2007.05.004} }