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This paper investigates the dynamic programming principle for a generalstochastic control problem in which the state processes are described by aforward-backward stochastic differential equation (FBSDE). Using the method ofS-topology, we show that there exists an optimal control for the valuefunction. Then a dynamic programming principle is established. As aconsequence, an extended Hamilton-Jacobi-Bellman (HJB) equation is derived. Theexistence and uniqueness of both smooth solution and a new type of viscositysolution are investigated for this extended HJB equation. Compared with theextant researches on stochastic maximum principle, this paper is the firstnormal work on partial differential equation (PDE) method for a controlledFBSDE system.

Dynamic programming principle for a controlled FBSDE system and associated extended HJB equation