Abstract
Building on previous results of the author this paper presents two new error estimates for the reachable set of an affine control system if only piece-wise constant admissible controls on a uniform mesh are used instead of all measurable admissible controls. It is natural to expect that the resulting “shrinkage” of the reachable set is of the order of the mesh size. In this paper it is proved that under certain reasonable conditions the error is of higher than first order.
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This paper is dedicated to the 70-th anniversary of Gustav Feichtinger.
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Veliov, V.M. On the relationship between continuous- and discrete-time control systems. Cent Eur J Oper Res 18, 511–523 (2010). https://doi.org/10.1007/s10100-010-0167-2
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DOI: https://doi.org/10.1007/s10100-010-0167-2