  In this paper, we study a stochastic recursive optimal control problem in
which the value functional is defined by the solution of a backward stochastic
differential equation (BSDE) under $\tilde{G}$-expectation. Under standard
assumptions, we establish the comparison theorem for this kind of BSDE and give
a novel and simple method to obtain the dynamic programming principle. Finally,
we prove that the value function is the unique viscosity solution of a type of
fully nonlinear HJB equation.
