# State observation and sensor selection for nonlinear networks

## TL;DR

This paper introduces an optimization-based method for observing states and selecting sensors in nonlinear networks, addressing fundamental limitations and demonstrating practical effectiveness in biological and combustion systems.

## Contribution

It presents a novel approach combining optimization and observability analysis for nonlinear networks, surpassing graph-theoretic methods and enabling better sensor placement.

## Key findings

- Identifies trade-offs between observed variables, observation length, and estimation error.
- Shows limitations of purely graph-theoretic observability in practical scenarios.
- Successfully finds key components in biological and combustion networks for full state estimation.

## Abstract

A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system. However, network states are usually unknown, and only a fraction of the state variables are directly measurable. The observability problem concerns reconstructing the network state from this limited information. Here, we propose a general optimization-based approach for observing the states of nonlinear networks and for optimally selecting the observed variables. Our results reveal several fundamental limitations in network observability, such as the trade-off between the fraction of observed variables and the observation length on one side, and the estimation error on the other side. We also show that owing to the crucial role played by the dynamics, purely graph- theoretic observability approaches cannot provide conclusions about one's practical ability to estimate the states. We demonstrate the effectiveness of our methods by finding the key components in biological and combustion reaction networks from which we determine the full system state. Our results can lead to the design of novel sensing principles that can greatly advance prediction and control of the dynamics of such networks.