Adaptive Estimation of Nonlinear Distributed Parameter Systems

  • Joseph Kazimir
  • I. G. Rosen
Conference paper
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 118)


The adaptive (on-line) estimation of parameters for a class of nonlinear distributed parameter systems is considered. A combined state and parameter estimator is constructed as an initial value problem for an infinite dimensional evolution equation. State convergence is established via a Lyapunov-like estimate. The finite dimensional notion of persistence of excitation is extended to the infinite dimensional case and used to establish parameter convergence. A finite dimensional approximation theory is presented and a convergence result is proven. An example involving the identification of a nonlinear heat equation is discussed and results of a numerical study are presented.

1991 Mathematics Subject Classification

93B30 93C25 93C20 65J10 

Key words and phrases

On-line estimation adaptive identification parameter convergence persistence of excitation distributed parameter systems infinite dimensional systems finite dimensional approximation 


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Copyright information

© Springer Basel AG 1994

Authors and Affiliations

  • Joseph Kazimir
    • 1
  • I. G. Rosen
    • 1
  1. 1.Center for Applied Mathematical Sciences Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA

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