Optimal sensor placement for state reconstruction of distributed process systems

Antonio A. Alonso, Christos E. Frouzakis, Ioannis G. Kevrekidis

Research output: Contribution to journalArticlepeer-review

79 Scopus citations


In this contribution we propose a systematic approach to field reconstruction of distributed process systems from a limited and usually reduced number of measurements. The method exploits the time scale separation property of dissipative processes and concepts derived from principal angles between subspaces, to optimally placing a given number of sensors in the spatial domain. Basic ingredients of the approach include the identification of a low-dimensional subspace capturing most of the relevant dynamic features of the distributed system, and the solution of a max-min optimization problem through a guided search technique. The low-dimensional subspace can be defined either through a spectral basis (eigenfunctions of a linear or linearized part of the operator) or through a semiempirical expansion known in the engineering literature as the Proper Orthogonal Decomposition (POD) or Karhunen-Loeve expansion. For both cases, the optimal sensor placement problem will be solved by taking advantage of the underlying algebraic structure of the low-dimensional subspace. The implications of this approach for dynamic observer design will be discussed together with examples illustrating the proposed methodology.

Original languageEnglish (US)
Pages (from-to)1438-1452
Number of pages15
JournalAIChE Journal
Issue number7
StatePublished - Jul 2004

All Science Journal Classification (ASJC) codes

  • Biotechnology
  • Environmental Engineering
  • General Chemical Engineering


  • Distributed process systems
  • Observer design
  • Optimal sensor placement
  • Proper orthogonal decomposition
  • Spectral decomposition


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