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Asymptotic Theory of the Reachable Sets to Linear Periodic Impulsive Control Systems

Авторы: Goncharova E., Ovseevich A.

Журнал: Proc. of 5th Intern. Conf. on Informatics in Control, Automation and Robotics (ICINCO 2008, Funchal, Madeira (Portugal), May 11–15, 2008)

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Год: 2008

Отчётный год: 2008

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Местоположение издательства: Funchal, Madeira

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Аннотация: We study linear periodic control systems with a bounded total impulse of control. The main result is an asymptotic formula for the reachable set, which, at the same time, reveals the structure of the attractor - the set of all limit shapes of the reachable sets. The attractor is shown to be parameterized by a (finite-dimensional) toric fibre bundle over a circle. The fibre of the bundle can be described via the Floquet multipliers (monodromy matrix) of the linear system. Moreover, the limit dynamics of shapes of reachable sets can be parametrized by an explicit curve on the toric bundle.

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