  In this paper, we study the question of existence and uniqueness of solution
of neutral stochastic functional differential equations driven by G- Brownian
motion (GNSFDEs in short) on Banach space driven by relaxed controls in which
the neutral term and diffusion do not depend on the control variable. By using
tightness techniques and the weak convergence techniques for each probability
measure in the set of all possible probabilities of our dynamic, we prove the
existence of an optimal relaxed control. A motivation of are work is presented
and a Numerical analysis for the uncontrolled G-NSFDE is given.
