  This paper is concerned with optimal control of systems driven by
G-stochastic differential equations (G-SDEs), with controlled jump term. We
study the relaxed problem, in which admissible controls are measurevalued
processes and the state variable is governed by an G-SDE driven by a counting
measure valued process called relaxed Poisson measure such that the compensator
is a product measure. Under some conditions on the coefficients, using the
G-chattering lemma, we show that the strict and the relaxed control problems
have the same value function. Additionally, we derive a maximum principle for
this relaxed problem.
