Observability analysis and observer design of networks of R\"ossler systems

We address the problem of retrieving the full state of a network of R\"ossler systems from the knowledge of the actual state of a limited set of nodes. The selection of the nodes where sensors are placed is carried out in a hierarchical way through a procedure based on graphical and symbolic observability approaches. By using a map directly obtained from the governing equations, we design a nonlinear network observer which is able to unfold the state of the non measured nodes with minimal error. For sparse networks, the number of sensors scales with half the network size and node reconstruction errors are lower in networks with heterogeneous degree distributions. The method performs well even in the presence of parameter mismatch and non-coherent dynamics and, therefore, we expect it to be useful for designing robust network control laws.