Asymptotic control theory for a system of linear oscillatorsстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 17 января 2018 г.
Аннотация:We present an asymptotic control theory for a system of an arbitrary number of linear oscillators under a common bounded control. We suggest a design method of a feedback control for this system. By using the DiPerna-Lions theory of singular ODEs, we prove that the suggested control law correctly defines the motion of the system. The obtained control is asymptotically optimal: the ratio of the motion time to zero under this control to the minimum one is close to 1 if the initial energy of the system is large. The results are partially based on a new perturbation theory of observable linear systems.