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APICS Research team

Analysis and Problems of Inverse type in Control and Signal processing

  • Leader : Laurent Baratchart
  • Research center(s) : CRI Sophia Antipolis - Méditerranée
  • Field : Applied Mathematics, Computation and Simulation
  • Theme : Optimization and control of dynamic systems

Team presentation

APICS' main endeavor is to show that certain techniques from harmonic analysis, approximation theory, and differential geometry can be made effective for identification and control of dynamical systems.

APICS is involved with identification and design issues for linear systems in the frequency domain (i.e. 1-D deconvolution), thereby continuing former work by Miaou.Applications thereof deal mainly with the design of resonnant and surface acoustic waves filters. Meanwhile, APICS has broaden its scientific scope by considering inverse source and free-boundary problems for elliptic equations in 2-D and 3-D, with emphasis on the Laplacian and conductivity equations.Applications concern electro-encephalography, non-destructive control, and the localization of free-boundaries, for instance in magnetic confinement of plasmas.

Research themes

  • Inverse potential problems. Recall that, being given an elliptic operator, a potential is generated by the convolution product between one of its fundamental solution and a measure. The related inverse problem then consists in recovering the measure from the knowledge of its potential. It appears naturally in geophysical or electricomagnetical issues, and more generally in non-destructive control, whivh is one of APICS's main applications field.
  • Frequency design and synthesis. The key remark here is that the transfer function of a stable causal linear system can be looked upon as a functional object with some analyticity properties. Part of the work consists in proposing a reconstruction process of the transfer function, starting with a set of pointwise measurements. A two step process has been set up; the transfer function is first sought as a function in a Hardy space (bounded extremal problem), then approximated as a rational function (possibly matrix-valued) of given McMillan degree. This has been implemented in softwares like Rarl2 and Presto-HF, that are of use nowadays at the production level to Alcatel-Alenia-Space. Apics is also engaged in the design and tuning of Surface Acoustic Wave filters.


International and industrial relations

  • CNES Toulouse (Microwave filters),
  • Alcatel-Alenia-Space Toulouse (Microwave filters)
  • Thales Airborne Systems (filtres micro-ondes)
  • Associate team with MIT and Vanderbilt University
  • Partnership with UPV Bilbao

Keywords: Identification Control Design Harmonic analysis Inverse elliptic problems Deconvolution Software