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Ensemble Control of Dynamic Systems with Square Impulses

Авторы: Staritsyn M., Goncharova E., Pereira F.L.

Журнал: IFAC-PapersOnLine

Том: 55

Номер: 16

Год: 2022

Отчётный год: 2022

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Теория и методы исследования эволюционных уравнений и управляемых систем с их приложениями

DOI: 10.1016/j.ifacol.2022.09.031

Аннотация: In the article, the basic mathematical concepts of quadratic-impulse control are extended to dynamical systems in the space of probability measures (local continuity equations) representing dynamic ensembles of (infinitely many) homotypic individuals. Starting from a model with quadratic dependence on an unbounded control, we constructively design its impulsive trajectory extension, which, as a byproduct, ensures also the well-posedness of an associated optimal control problem. The main attention is paid to the characteristic control ODE whose extension combines a discontinuous time change with a convexification of the velocity set via generalized controls. Finally, we show that it is possible to exclude the generalized controls and represent extended states as impulsive solutions of a measure-driven ODE. The resulting impulsive continuity equation can be viewed as a measure-driven equation in the space of measures.

Индексируется WOS: Q5

Индексируется Scopus: Нет

Индексируется УБС: Нет

Индексируется РИНЦ: Нет

Индексируется ВАК: Нет

Индексируется CORE: Нет

Публикация в печати: 0