  Trajectory optimization is a fundamental stochastic optimal control problem.
This paper deals with a trajectory optimization approach for dynamical systems
subject to measurement noise that can be fitted into linear time-varying
stochastic models. Exact/complete solutions to these kind of control problems
have been deemed analytically intractable in literature because they come under
the category of Partially Observable Markov Decision Processes (POMDPs).
Therefore, effective solutions with reasonable approximations are widely sought
for. We propose a reformulation of stochastic control in a reinforcement
learning setting. This type of formulation assimilates the benefits of
conventional optimal control procedure, with the advantages of maximum
likelihood approaches. Finally, an iterative trajectory optimization paradigm
called as Stochastic Optimal Control - Expectation Maximization (SOC-EM) is
put-forth. This trajectory optimization procedure exhibits better performance
in terms of reduction of cumulative cost-to-go which is proved both
theoretically and empirically. Furthermore, we also provide novel theoretical
work which is related to uniqueness of control parameter estimates. Analysis of
the control covariance matrix is presented, which handles stochasticity through
efficiently balancing exploration and exploitation.
