Observability analysis and state reconstruction for networks of nonlinear systems

We address the problem of retrieving the full state of a network of Rössler systems from the knowledge of the actual state of a limited set of nodes. The selection of nodes where sensors are placed is carried out in a hierarchical way through a procedure based on graphical and symbolic observability approaches applied to pairs of coupled dynamical systems. By using a map directly obtained from governing equations, we design a nonlinear network reconstructor that is able to unfold the state of non-measured nodes with working accuracy. For sparse networks, the number of sensor 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 for dynamical systems with completely different algebraic structures like the Hindmarsch-Rose; therefore, we expect it to be useful for designing robust network control laws.