Maximum principle for optimal control problem of stochastic delay differential equations driven by fractional Brownian motions

In this paper, we consider the optimal control problem for delayed stochastic differential equations driven by fractional Brownian motions. Some necessary Pontryagin's type conditions are derived by considering the adjoint equations satisfying an anticipated backward stochastic differential equation driven by both fractional Brownian motions and the standard Brownian motions. Some new results on stochastic analysis about the control systems driven by fractional Brownian motions are presented. As an application, a linear quadratic problem is deduced, and a numerical example is shown to prove the effectiveness of our method.