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

TL;DR

This paper develops necessary and sufficient conditions for near-optimal control of forward-backward stochastic differential systems with observation noise under partial information, using variational principles and convexity assumptions.

Contribution

It introduces a local necessary condition with an explicit error bound and a sufficient maximum principle for near-optimal control under partial information.

Findings

Established necessary conditions for ε-near optimal controls with an error order of ε^{1/2}.

Proved sufficiency of an ε-maximum principle under convexity conditions.

Extended control theory to systems with observation noise and partial information.

Abstract

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.