Impulsive Control Systems with Trajectories of Bounded p-Variation
Elena Goncharova, Olga Samsonyuk, Maxim Staritsyn
We address impulsive rough control systems, i.e., rough differential equations driven by discontinuous controls with bounded p-variation. The main results are: the existence of a unique solution under a discontinuous rough control, and a constructive representation of 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.