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Dynamical systems with states of bounded p-variation: A new trend in impulsive control

Авторы: Goncharova E., Samsonyuk O., Staritsyn M.

Журнал: Cybernetics and Physics

Том: 6

Номер: 4

Год: 2017

Отчётный год: 2017


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Аннотация: “Rough” differential equations form a class of control-affine dynamical systems driven by input signals of a low regularity, namely, paths of bounded p-variation (BV_p ), p > 1. In this paper, we address impulsive rough control systems, i.e., rough differential equations driven by discontinuous BV_p -controls. The main results are: the existence of a unique state solution under a discontinuous rough input, and a constructive representation of the system’s states. The representation is performed by a discrete-continuous equation involving a Young integral and the sum of jumps of a trajectory, defined by an auxiliary ordinary differential equation.

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