Information-theoretic approach to the study of control systems

We propose an information-theoretic framework for studying control systems, based on a model of controllers analogous to communication channels. Given the initial state of a system to be controlled, the dynamics of a controller is described as applying a transmission channel, called the actuation channel, to that state in order to redirect it towards another target state. In this process, two different control strategies can be adopted: (i) the controller applies an actuation dynamics independently of the state of the system to be controlled (open-loop control); or (ii) the controller enacts an actuation dynamics based on some information about the state of the controlled system (closed-loop control). In the context of this model, we provide necessary and sufficient entropic conditions for a system to be perfectly controllable and perfectly observable. Also, using the fact that the information gathered by a controller is quantified by mutual information, we prove a limiting result expressing the trade-off between the availability of information in a closed-loop control process and its performance over open-loop control in stabilizing a system. This work completes a first paper on the subject by providing new proofs of the results, and by proposing an information-based optimality criterion for control systems. New applications of this approach pertaining to proportional controllers, and the control of chaotic maps are also presented