Carlos Canudas de Wit was a speaker during the Workshop “Resilient Control of Infrastructure Networks” organized by Politecnico di Torino.

The talk was about “Scales Paradigms in Large-scale networks”

The talk deals with the problems of controlling/observing aggregates of large-scale complex systems with a scarce number of actuators and sensors. Aggregates here are “aggregated” variables functions of the systems state-space variables such as mean values. Examples of such a class of systems are traffic networks, Brain neural networks, heating systems, among others. The basic idea is to devise a “virtual” aggregated model of the original large-scale system using the scale-free (SF) metric, which indicate that the degree distributions of the associated graph follows an exponential decaying law. Then, we discuss different partitioning algorithms leading to aggregated graphs with the SF desired distribution. In the talk, I also present the mathematical properties necessary for the average observability/detectability and in particular, the graph’s structure needed to such properties to hold. Finally, an example will be given in network epidemiology where a partition algorithm can include the observability conditions and an observed can be designed using boundary measures. In the second part of the talk, I present a different alternative for reducing system complexity, which consist in representing a large traffic network as a continuum. That is, to approximate a large-scale dynamic graph (where each node represent a variable), by a Partial Differential equation. The objective of this second approach is to use the PDE model for designing boundary estimators and control. This is work in progress