Partial Information Near-Optimal Control of Forward-Backward Stochastic Differential System with Observation Noise

This paper first makes an attempt to investigate the partial information near optimal control of systems governed by forward-backward stochastic differential equations with observation noise under the assumption of a convex control domain. By Ekeland's variational principle and some basic estimates for state processes and adjoint processes, we establish the necessary conditions for any $\varepsilon$-near optimal control in a local form with an error order of exact \varepsilon ^{% \frac{1}{2}}. Moreover, under additional convexity conditions on Hamiltonian function, we prove that an $\varepsilon$-maximum condition in terms of the Hamiltonian in the integral form is sufficient for near-optimality.