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• W3216421739 abstract "We present (mathbf{OURS} ), a precision-oriented (mathbf{MATLAB} ) tool for computing Open image in new window ver- and Open image in new window nder- approximations of Open image in new window eachable Open image in new window ets for analytic time-invariant differential equations. The main theoretical framework behind (mathbf{OURS} ) is introduced, including the concept of evolution function, whose zero sub-level sets are used to describe reachable sets, and a series representation of evolution function. Using the partial sums of this series, (mathbf{OURS} ) finds over- and under-approximations of evolution function at time-instants: it consecutively estimates each remainder of the corresponding partial sum of the series with interval arithmetics until one remainder satisfies the designated precision, and then builds over- and under-approximations with this remainder. The structure of (mathbf{OURS} ) is also presented, such as the forms of inputs and outputs, and technical implementations of the crucial steps inside. We also compare (mathbf{OURS} ) with two other existing methods." @default.
• W3216421739 created "2021-12-06" @default.
• W3216421739 creator A5014613783 @default.
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• W3216421739 date "2021-01-01" @default.
• W3216421739 modified "2023-10-16" @default.
• W3216421739 title "$$mathbf{OURS} $$: Over- and Under-Approximating Reachable Sets for Analytic Time-Invariant Differential Equations" @default.
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• W3216421739 doi "https://doi.org/10.1007/978-3-030-91265-9_14" @default.
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