  We consider a robust impulse control problem in finite horizon where the
underlying uncertainty stems from an impulsively and continuously controlled
functional stochastic differential equation (FSDE) driven by Brownian motion.
We assume that the controller acts upon the system by impulses while the
adversary player (nature) acts through continuous controls. We look for a weak
solution which leads us to consider a system of sequentially interconnected,
obliquely reflected backward stochastic differential equations (RBSDEs) with
stochastic Lipschitz coefficients. We show existence of solutions to our system
of RBSDEs by applying a Picard iteration approach. Uniqueness then follows by
relating the limit to an auxiliary impulse control problem.
