Information transfer in stochastic optimal control with randomized strategies and directed information criterion

We show that stochastic dynamical control systems are capable of information transfer from control processes to output processes, with operational meaning as defined by Shannon. Moreover, we show that optimal control strategies have a dual role, specifically, (i) to transfer information from the control process to the output process, and (ii) to stabilize the output process. We illustrate that information transfer is feasible by considering general Gaussian Linear Decision Models, and relate it to the well-known Linear-Quadratic-Gaussian (LQG) control theory.