Hierarchical decomposition of optimal control and information strategies in control-coding capacity of stochastic systems

The Control-Coding Capacity (CC Capacity) is defined as the maximum amount of information in bits/second, which can be encoded into randomized control strategies, transmitted over the control system, and decoded at its outputs, with arbitrary asymptotic small probability of error. This paper shows that optimal randomized control strategies which achieve the CC Capacity impose a natural hierarchical decomposition into two simpler sub-optimization problems, one related to the control objectives and one related to the information transmission objectives. The hierarchical decomposition states that control signals and communication signals interact in a specific order, optimal strategies are decentralized, and the information transmission rate is zero, unless the power allocated to the overall system is above a certain threshold, which is the minimum cost to achieve the control objectives.