Abstract
In this chapter, we consider reachability methods that characterize how a set centered around a system trajectory grows or contracts as the trajectory evolves. In particular, we consider interval growth bounds, which characterize the growth and contraction of intervals. An interval over-approximation of the reachable set from an interval of initial states can be obtained by computing a single successor state from the center of the initial set and bounding the growth of neighboring trajectories. We first describe the general method for over-approximating reachable sets with interval growth bounds. Then, we describe three methods to compute such growth bounds: from a matrix measure of the state Jacobian matrix; from a componentwise upper bound on the state Jacobian matrix; and from matrix measures of a blockwise partition of the state Jacobian matrix to allow for a greater flexibility in computational efficiency and conservativeness.
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Meyer, PJ., Devonport, A., Arcak, M. (2021). Growth Bounds. In: Interval Reachability Analysis. SpringerBriefs in Electrical and Computer Engineering(). Springer, Cham. https://doi.org/10.1007/978-3-030-65110-7_6
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DOI: https://doi.org/10.1007/978-3-030-65110-7_6
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Online ISBN: 978-3-030-65110-7
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