Optimal control and signaling strategies ofcontrol-coding capacity of general decisionmodels: applications to gaussian models anddecentralized strategies

We investigate the control-coding (CC) capacity of general dynamical decision models(DMs) that involve nonlinear filtering, which is absent in the specific DMs investigated in [C. K.Kourtellaris and C. D. Charalambous,IEEE Trans. Inform. Theory, 64 (2018), pp. 4962--4992]. Wederive characterizations of CC capacity and we show their equivalence to extremum problems ofmaximizing the information theoretic measure of directed information from the input process to theoutput process of the DM over randomized strategies. Due to the generality of the DMs, the CCcapacity is shown to be equivalent to partially observable Markov decision problems, contrary to theDMs in the above mentioned paper, which give rise to fully observable Markov decision problems.Subsequently, the CC capacity is transformed, using nonlinear filtering theory, to fully observableMarkov decision problems. For the application example of a Gaussian DM with past dependenceon inputs and outputs, we prove a decentralized separation principle that states optimal inputsare Gaussian and consist of (i) a control, (ii) an estimation, and (iii) an information transmissionpart, which interact in a specific order. The optimal control and estimation parts are related tolinear-quadratic Gaussian stochastic optimal control problems with partial information. Variousdegenerated cases are discussed, including examples from the above mentioned paper, which do notinvolve estimation.