Relationship between MP and DPP for stochastic recursive optimal control problem under volatility uncertainty

In this paper, we study the relationship between maximum principle (MP) and dynamic programming principle (DPP) for stochastic recursive optimal control problem driven by $G$-Brownian motion. Under the smooth assumption for the value function, we obtain the connection between MP and DPP under a reference probability $P_{t,x}^{\ast}$. Within the framework of viscosity solution, we establish the relation between the first-order super-jet, sub-jet of the value function and the solution to the adjoint equation respectively.