In this thesis, a new inference-based solution to stochastic optimal control (SOC) for general nonlinear systems is developed. This novel method applies to standard SOC problem, as well as robust and risk-seeking variations. The presented approach uniﬁes many existing works, and makes possible, inference-based approximations to be applied to robust, risk-seeking, and standard SOC problems. Thus, an approximate method based on extended Kalman ﬁltering is developed and tested on the inverted pendulum problem, and compared with existing methods. As an application, the developed algorithm was adapted to a practically important problem in visual control in robotics known as image-based visual servoing (IBVS). The proposed control methodology for visual servoing was implemented for real-time experiments, and was compared with the standard IBVS methodology. The experimental results show that the proposed method can improve the myopic behaviors of standard IBVS methodology.