Rough Paths Theory and Impulsive Control: A Promising Connection

作     者：Samsonyuk, Olga N. Staritsyn, Maxim V. 

作者机构：Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of the Russian Academy of Sciences Irkutsk Russia 

出 版 物：《IFAC-PapersOnLine》 

年 卷 期：2018年第51卷第32期

页      面：615-618页

核心收录：

主　　题：Integral equations Differential equations Dynamical systems Constructive representation Driven system Impulsive controls Input affine Mathematical theory Rough differential equations Rough paths Vector valued 

摘      要：This short discussion note is devoted to establishing some connections between the framework of dynamical systems driven by signals of a low regularity (rough differential equations) and the mathematical theory of impulsive control (measure-driven systems), which, as we believe, would essentially enrich one another. More precisely, we attempt to elaborate an impulsive (discontinuous) extension of the theory of rough differential equation for input-affine models with states of unbounded first variation. In the paper, we are focused on a concept of solution for impulsive rough differential equations with vector-valued controls of bounded p-variation, p£ (1,2), and its constructive representation through a (discrete-continuous) Young s integral equation. © 2018