Locality in Gramian Observation for Complex Networked Systems

The observability of large-scale complex networks is fundamental for studying and controlling the dynamic behavior of intricate social, biological, and infrastructural systems. The key is to infer the internal system states through the sensor measuring. However, existing methods fall short in high sensor deployment costs, low computational efficiency, and limited network observation performance. To meet these challenges, this paper proposes an optimal sensor placement scheme based on network locality. The observability of network states under specific sensor configurations is quantified by computing the minimum eigenvalue of the observability Gramian. Then, the sensor placement problem is reformed as the optimization of sensor set functions based on the observability Gramian. In addition, an efficient and scalable algorithm is developed to derive the near-optimal solution. Experimental results show that the proposed near-optimal sensor placement strategy achieves superior observability performance while deploying an equivalent number of sensors, substantially reducing computational requirements.