Optimality of integrated process networks

We introduce a new framework for distributed control and optimization of complex networks. Conservation laws for extensive quantities and the second law of thermodynamics lead to conditions for stability and optimality of the network. We derive a general way of describing interconnections in networks through matrix representations that capture a network´s topology using basic principles from electrical engineering methodologies. This shows how the dynamics of independent entities in a network define the objective function of the optimization problem that is simultaneously solved. A generalized version of Tellegen´s theorem from electrical circuit theory plays a central role in developing the objective function of the regarded dynamic networks. These results indicate that we can solve optimization problems using dynamical systems, and how the objective function depends on the choice of feedback control and strategies. Examples are presented to illustrate these principles for different types of network connections, both for transient and stationary conditions. We apply the introduced theory to business systems integrated into larger logistic systems.