Страница публикации

A note on differential-algebraic systems with impulsive and hysteresis phenomena

Тип публикации: Статья в журнале

Тип материала: Текст

Авторы: Petrenko P., Samsonyuk O., Staritsyn M.

Журнал: Cybernetics and Physics

Язык публикации: english

Том: 9

Номера страниц: 51-56

Количество страниц: 6

Номер: 1

Год публикации: 2020

Отчетный год: 2020

Аннотация: In this note, we single out some promising classes of differential-algebraic equations (DAEs) with hysteresis phenomena, and propose their meaningful generaliza-tions. We consider DAEs of index 2 having two fea-tures: i) non-linearity of hysteresis type modeled by a sweeping process, and ii) impulsive control represented by a bounded signed Borel measure. For such a DAE, we design an equivalent structural form, based on the Kronecker-Weierstrass transformation, and prove a necessary and sufficient condition for the existence and uniqueness of a solution to an initial value problem. We propose a notion of generalized solution to a DAE as a realization of impulsive trajectory relaxation. This relaxation is described by a dynamical system with states of bounded variation and can be equivalently represented as a system of “ordinary” DAEs.

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