  State estimation and sensor selection problems for nonlinear networks and
systems 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 results
when applied to nonlinear network dynamics. In addition, state estimation and
sensor selection problems are often treated separately, and this might decrease
the overall estimation performance. To address these challenges, we develop a
novel methodology for selecting sensor nodes for networks with nonlinear
dynamics. Our main idea is to incorporate the sensor selection problem into an
initial state estimation problem. The resulting mixed-integer nonlinear
optimization problem is approximately solved using three methods. The good
numerical performance of our approach is demonstrated by testing the algorithms
on prototypical Duffing oscillator, associative memory, and chemical reaction
networks. The developed codes are available online.
