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State estimation and sensor selection problems for nonlinear networks andsystems are ubiquitous problems that are important for the control, monitoring,analysis, and prediction of a large number of engineered and physical systems.Sensor selection problems are extensively studied for linear networks. However,less attention has been dedicated to networks with nonlinear dynamics.Furthermore, widely used sensor selection methods relying on structural(graph-based) observability approaches might produce far from optimal resultswhen applied to nonlinear network dynamics. In addition, state estimation andsensor selection problems are often treated separately, and this might decreasethe overall estimation performance. To address these challenges, we develop anovel methodology for selecting sensor nodes for networks with nonlineardynamics. Our main idea is to incorporate the sensor selection problem into aninitial state estimation problem. The resulting mixed-integer nonlinearoptimization problem is approximately solved using three methods. The goodnumerical performance of our approach is demonstrated by testing the algorithmson prototypical Duffing oscillator, associative memory, and chemical reactionnetworks. The developed codes are available online.

Joint Sensor Node Selection and State Estimation for Nonlinear Networks and Systems