Partially observed stochastic bilinear system control

Semi-explicit solution to a partially observed stochastic bilinear system control problem is given. The system is bilinear in respect to the control inputs, and corrupted by additive Wiener processes in the state and measurements equations. Beside the unobserved state the initial state is an unknown parameter. The optimal controls in a mean square sense are derived in dependence on the optimal value function that is solved numerically from the Bellman equation and saved in a look-up table for prompt calculation of optimal controls afterwards. The control effect is demonstrated in a simulation experiment where the controls remove the initial uncertainty and stabilise the process at the target level effectively.