This monograph describes the development of a theoretical framework for analysis of network information systems using the theories of dynamical systems and control. Examples of network information systems include large-scale interconnected systems such as air traffic control, communications, power and energy grid operations as well as many kinds of biological networks.

The authors describe a paradigm for their approach to the nonlinear analysis and control law design of large-scale network systems with many autonomous agents. Their goal is to develop a unified thermodynamic analysis and a framework for control system design of continuous-time, discrete-time and hybrid systems in the presence of a specified level of modeling uncertainty. 

For networks of interconnected dynamical systems, it is often desirable for some property of each subsystem to approach a single common value across the network.  This eventually leads to a need to establish a kind of distributed consensus across the network.  Previous approaches to this problem have used algebraic graph theory. Here the authors propose a new approach based on system thermodynamics, one that brings together classical thermodynamics and dynamical systems theory applied to the flow of information. Control algorithms inspired by thermodynamics are employed to address interactions between agents, cooperative and noncooperative control, task assignments and resource allocations.

This is clearly an advanced treatise that demands at least a good background in dynamical systems and control theory. It is another in a group of recent books  (Dynamics and Bifurcation in Networks by Martin Golubitsky and Ian Stewart, for example) that attempt to provide foundations for the analysis of large networks of dynamical systems. 

After setting up their thermodynamic approach, the authors conduct an extensive analysis of the many stability and robustness questions that can arise in networks of both continuous and discrete dynamical systems and the associated control theory questions.

Bill Satzer (bsatzer@gmail.com), now retired from 3M Company, spent most of his career as a mathematician working in industry on a variety of applications. He did his PhD work in dynamical systems and celestial mechanics.