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Asymptotics for Singularly Perturbed Reachable Sets

Авторы: Goncharova E., Ovseevich A.

Журнал: Lecture Notes in Computer Science

Том: 5910

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Год: 2010

Отчётный год: 2010

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Аннотация: 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 E tends to 0, and the rate of convergence is O(epsilon(alpha)), where 0 < alpha < 1 is arbitrary. In fact, the said rate of convergence is log 1/epsilon. Under an extra. smoothness assumption we find the coefficient of epsilon log 1/epsilon in the asymptotics of the support function of the reachable set.

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