Abstract
We study, in the spirit of [1], reachable sets for singularly perturbed linear control systems. The fast component of the phase vector is assumed to be governed by a strictly stable linear system. It is shown in loc.cit. that the reachable sets converge as the small parameter ε tends to 0, and the rate of convergence is O(ε α), where 0 < α< 1 is arbitrary. In fact, the said rate of convergence is εlog1/ε. Under an extra smoothness assumption we find the coefficient of εlog1/ε in the asymptotics of the support function of the reachable set.
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Goncharova, E., Ovseevich, A. (2010). Asymptotics for Singularly Perturbed Reachable Sets. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2009. Lecture Notes in Computer Science, vol 5910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12535-5_32
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DOI: https://doi.org/10.1007/978-3-642-12535-5_32
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