Generalized solutions of bounded p-variation of nonlinear control systems and nonsmooth optimal impulsive control problems

摘要

The paper deals with control impulsive “rough” differential equations, namely, dynamical systems driven by discontinuous control inputs of bounded p-variation, p ≥ 1. For p ϵ [1, 2), we prove the existence of a solution to the impulsive rough differential equation and perform its constructive representation by a discrete-continuous equation involving a Young integral and the sum of jumps of a state, described by an auxiliary ODE. Finally, we state an optimal impulsive control problem for the rough dynamical system, and prove the existence of a minimizer.