Interdependence of Control and Communications in Cyber Physical Systems: From Maxwell's Demon to Diffusion

In order to understand how to operate the physical dynamics of cyber physical systems (CPSs), we study the control of entropy (or equivalently uncertainty) via communications in CPSs. We consider the controller as the Maxwell's demon that decimates the system entropy. Due to the second law of thermodynamics, the system entropy cannot be spontaneously decreased. Therefore, to reduce the system entropy, the controller needs external information communicated from sensors. The following aspects of the proposed framework will be introduced: (a) For a finite state physical system in CPS, we derive upper and lower bounds for the communication requirements. The optimal designs of message mechanism and control policy are proposed. (b) For networked physical dynamics nodes (such as generators in a power grid), the entropy propagation is described using ordinary differential equations, in which the communication requirement due to quantization error is taken into account. (c) Networked CPS is condensed to the continuous space and the corresponding entropy evolution is described using partial differential equations (PDEs), for two special types of CPS dynamics. Solutions are obtained for the PDEs to characterize the propagation, decimation and generation of entropy in the field.