Control-Coding Capacity of Decision Models Driven by Correlated Noise and Gaussian Application Examples

Abstract

We characterize the n -finite time feedback information (FTFI) control-coding capacity of decision models (DMs) driven by correlated noise. Under information stability the per unit limit, called control-coding (CC) capacity of the DM is operational, and analogous to Shannon's coding capacity of noisy communication channels, with the encoder replaced by a controller-encoder. We also analyze application examples of recursive linear DMs driven by correlated Gaussian noise, subject to an average cost constraint of quadratic form, called linear-quadratic Gaussian DMs (LQG-DMs). In one of the main theorems we show that the optimal randomized control strategies that achieve the n -FTFI CC capacity of the LQG-DMs, consist of multiple parts, that include control, estimation, and information transmission/signalling strategies, and that these strategies are determined using decentralized optimization techniques.