Adaptive observer for a class of parabolic PDEs

T. Ahmed-Ali, F. Giri, M. Krstic, F. Lamnabhi-Lagarrigue, L. Burlion

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


The problem of state observation, based on spatiallysampled output measurements, is addressed for a class of infinite dimensional systems, modelled by a semi-linear heat equation augmented with a structured uncertain part involving a set of unknown parameters. An adaptive observer is designed that provides online estimates of the system (spatially distributed) state and unknown parameters based on sampled data (in space). Sufficient conditions for the observer to be exponentially convergent are established. These include an ad-hoc persistent excitation condition as well as a condition on how the observer gain must be selected in relation with the space sampling interval.

Original languageEnglish (US)
Article number7329949
Pages (from-to)3083-3090
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number10
StatePublished - 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications


  • Nonlinear system
  • Observer design
  • PDE systems


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