Signalling and Control of Nonlinear Partially Observable Stochastic Control Models

We characterize the signalling and control rate of nonlinear partially observable stochastic control or decision models (DMs), called operational control-coding (CC) capacity. This is defined as the maximum signalling rate in bits/second, of encoding information signals into randomized control strategies, and reproducing them asymptotically at the output of the DM, with arbitrary small error probability. We show that the CC capacity is characterized by an extremum problem of an information theoretic pay-off, with information state the posteriori distribution of nonlinear filtering, subject to an average cost constraint. The dual of the CC capacity is characterized by the minimization of the average cost subject to a rate constraint. As an application example, we consider the partially observable, linear-quadratic Gaussian (LQG)-DM. We show that optimal randomized control strategies consist of an estimation and control part which controls the unobserved state of the DM, and an information transmission/signalling part which signals information through the DM.