Structural accessibility and structural observability of nonlinear networked systems
This provides a theoretical foundation for controlling and observing nonlinear networked systems, which is relevant for network science and complex systems researchers.
The authors extend structural controllability and observability to nonlinear networked systems, introducing and characterizing structural accessibility and structural observability. They show that nonlinearities reduce the number of variables needed for direct control and measurement.
The classical notions of structural controllability and structural observability are receiving increasing attention in Network Science, since they provide a mathematical basis to answer how the network structure of a dynamic system affects its controllability and observability properties. However, these two notions are formulated assuming systems with linear dynamics, which significantly limit their applicability. To overcome this limitation, here we introduce and fully characterize the notions "structural accessibility" and "structural observability" for systems with nonlinear dynamics. We show how nonlinearities make easier the problem of controlling and observing networked systems, reducing the number of variables that are necessary to directly control and directly measure. Our results contribute to understanding better the role that the network structure and nonlinearities play in our ability to control and observe complex dynamic systems.