Dynamical systems with states of bounded p-variation: A new trend in impulsive control
“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 (BVp), p > 1. In this paper, we address impulsive rough control systems, i.e., rough differential equations driven by discontinuous BVp-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.
CYBERNETICS AND PHYSICS, Vol. 6, No. 4, pp.208-214