Decoupling multivariate functions: a linearization approach

Philippe Dreesen, Mariya Ishteva, Joannes Schoukens

Research output: Chapter in Book/Report/Conference proceedingMeeting abstract (Book)


Block-oriented non-linear system identification uses static non-linear multivariate functions to describe the non-linear effects in a system. For the non-linear blocks the identification procedure provides a multiple input multiple output static mapping where in general a coupling exists between the variables (e.g., in the case of multivariate polynomials cross-terms between the input variables show up). For the sake of model interpretability, as well as to avoid the curse of dimensionality, it is desirable to find an equivalent parsimonious description where the non-linear functions are decoupled in a set of parallel single input single output mappings acting between some unknown internal variables (that are related to the inputs and outputs by means of unknown linear transformation matrices). We solve this decoupling task by means of a linearization approach: the first-order behavior of the multivariate functions is obtained in a set of operating points (this procedure is similar to constructing the small-signal model of a nonlinear element). The decoupling task then immediately leads to a simultaneous matrix diagonalization problem from which the unknown linear transformations follow, as well as the internal univariate mappings.
Original languageEnglish
Title of host publicationPresentation of poster at ERNSI 2014, European Research Network on System Identification, Oostende, Belgium, September 21-24, 2014
Publication statusPublished - 21 Sep 2014
EventERNSI 2014 - Thermae Palace Hotel, Ostend, Belgium
Duration: 21 Sep 201424 Sep 2014


WorkshopERNSI 2014
OtherModelling of dynamical systems is fundamental in almost all disciplines of science and engineering, ranging from life science to plant-wide process control. Engineering uses models for the design and analysis of complex technical systems. System identification concerns the construction, estimation and validation of mathematical models of dynamical physical or engineering phenomena from experimental data. This is the 23rd version of the European Workshop on System Identification, the first one being held in Saint-Malo in 1992. All through these years the workshop has maintained the scope of bringing together European researchers in the area of System Identification, in an informal setting that gives ample opportunities for participants to meet. The workshop program is composed of lectures from invited speakers, lectures from members of the ERNSI community, and poster presentations by -particularly- the PhD students and postdocs that are active in the network.


  • Block-oriented non-linear system identification
  • decoupling task


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