  This paper presents convergence analysis of a novel data-driven feedback
control algorithm designed for generating online controls based on partial
noisy observational data. The algorithm comprises a particle filter-enabled
state estimation component, estimating the controlled system's state via
indirect observations, alongside an efficient stochastic maximum principle type
optimal control solver. By integrating weak convergence techniques for the
particle filter with convergence analysis for the stochastic maximum principle
control solver, we derive a weak convergence result for the optimization
procedure in search of optimal data-driven feedback control. Numerical
experiments are performed to validate the theoretical findings.
