Hierarchical optimality of linear controllers-encoders-decoders operating at control-coding capacity of LQG control systems

Randomized control strategies which achieve the Control-Coding Capacity of Linear Quadratic Gaussian Control systems with complete information, are transformed, hierarchically into controller-encoder strategies, which stabilize the control system, encode information signals, and operate at the control-coding capacity. Further, it is shown that among all controllers, encoders and decoders which minimize Mean Square Error (MSE), the conditional mean decoder is optimal and linear controller-encoder-decoders are optimal.