Thermodynamics-based network systems control by thermal analogy

The laws of thermodynamics define the concepts of thermal equilibrium and thermal energy, and determine whether a particular transfer of thermal energy can occur. Collectively, these laws imply that a closed collection of thermodynamic subsystems will tend to energy equipartition. That is, the system will tend towards a condition where energy is evenly distributed over all subsystems. Applied to conductive heat transfer in a connected network of lumped thermal masses, the laws of thermodynamics imply that the system will approach thermal equilibrium. This paper generalizes the concepts of energy and entropy to undirected and directed networks of single integrators, and demonstrates how thermodynamic principles embodied by the laws of conductive heat transfer may be applied to the design of distributed consensus control algorithms for networked dynamic systems.