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Linear fractional LPV model identification from local experiments using an H∞-based glocal approach

Linear fractional LPV model identification from local experiments using an H∞-based glocal approach

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In this chapter a new identification technique is introduced to estimate a linear fractional representation (LFR) of a linear parameter-varying (LPV) system from local experiments using a dedicated non-smooth optimization procedure. Having access to a reliable set of local models, this technique consists more specifically in optimizing an H-norm-based cost function measuring the fit between the local information (represented by the locally estimated LTI models) and the local behavior of a parameterized global LPV model. The method presented in this chapter results directly in an LPV model whose parametric matrices can be rational functions of the scheduling variables without any interpolation step (required usually by the local approach) and without writing the local fully parameterized LTI state-space models with respect to a coherent basis. On top of that, specific attention is paid to parameterized LPV models satisfying a fully parameterized or a physically structured linear fractional representation. This identification procedure is tested and validated with a simulation example.

Chapter Contents:

  • Abstract
  • 9.1 Introduction
  • 9.2 Identification method
  • 9.2.1 Problem formulation, definitions, and notations
  • 9.2.2 Determination of the structure of G (s,_(pi),_)
  • 9.2.3 H∞-based optimization technique
  • 9.2.4 Computing the H∞-norm
  • 9.2.5 Minimizing the H∞-norm
  • 9.3 Identification results
  • 9.3.1 System description
  • 9.3.2 Linear fractional LPV model identification
  • 9.3.3 Validation
  • 9.4 Conclusions
  • References

Inspec keywords: H∞ control; linear parameter varying systems; optimisation; scheduling; identification; interpolation; state-space methods; matrix algebra

Other keywords: interpolation step; rational function; LFR; LTI state-space model; scheduling variable; H∞-norm-based cost function; parameterized global LPV model; identification technique; linear fractional representation; H∞-based glocal approach; identification procedure; LPV system; linear fractional LPV model identification; dedicated nonsmooth optimization procedure; parametric matrices; LTI model; linear parameter-varying system; parameterized LPV model

Subjects: Optimal control; Optimisation techniques; Algebra; Simulation, modelling and identification; Control system analysis and synthesis methods; Interpolation and function approximation (numerical analysis)

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