State Observation and Sensor Selection for Nonlinear Networks

Aleksandar Haber*, Ferenc Molnar, Adilson E. Motter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


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 tradeoff 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.

Original languageEnglish (US)
Pages (from-to)694-708
Number of pages15
JournalIEEE Transactions on Control of Network Systems
Issue number2
StatePublished - Jun 2018


  • Complex networks
  • observability
  • sensor selection
  • state and parameter estimation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Computer Networks and Communications
  • Control and Optimization


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