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

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