Observability analysis and state reconstruction for networks of nonlinear systems

Area of Science:

• Complex Systems
• Network Science
• Dynamical Systems Theory

Background:

• Understanding the behavior of large-scale dynamical networks is crucial for many scientific and engineering applications.
• However, monitoring the complete state of all network components is often infeasible due to sensor limitations.
• Existing methods may struggle with complex network topologies and noisy data.

Purpose of the Study:

• To develop a robust method for reconstructing the full state of a network from partial observations.
• To identify optimal sensor placement strategies for accurate state estimation.
• To validate the method's performance across different network structures and dynamical systems.

Main Methods:

• A hierarchical node selection procedure based on graphical and symbolic observability of coupled dynamical systems.
• Design of a nonlinear network reconstructor utilizing governing equations for state estimation.
• Analysis of network reconstruction accuracy concerning network sparsity and degree distribution heterogeneity.

Main Results:

• The proposed method accurately reconstructs the state of unmeasured nodes in Rössler systems.
• Sensor requirements scale linearly with network size for sparse networks.
• Lower reconstruction errors are observed in networks with heterogeneous degree distributions.
• The method demonstrates robustness to parameter mismatch and non-coherent dynamics.

Conclusions:

• The developed nonlinear network reconstructor effectively estimates the state of unmonitored nodes using limited sensor data.
• Optimal sensor placement strategies enhance reconstruction accuracy, particularly in sparse and heterogeneous networks.
• The method's applicability extends to diverse dynamical systems, suggesting potential for robust network control law design.