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Necessary conditions for optimality in the identification of elliptic systems with parameter constraints

  • W. H. Yu
Contributed Papers

Abstract

We consider the problems of dientifying the parametersa ij (x), b i (x), c(x) in a 2nd order, linear, uniformly elliptic equation,
$$\begin{gathered} - \partial _i (a_{ij} (x)\partial _j u) + b_i (x)\partial _i u + c(x)u = f(x),in\Omega , \hfill \\ \partial _v u|_{\partial \Omega } = \phi (s),s \in \partial \Omega , \hfill \\ \end{gathered} $$
on the basis of measurement data
$$u(s) = z(s),s \in B \subset \partial \Omega ,$$
with an equality constraint and inequality constraints on the parameters. The cost functionals are one-sided Gâteaux differentiable with respect to the state variables and the parameters. Using the Duboviskii-Milyutin lemma, we get maximum principles for the identification problems, which are necessary conditions for the existence of optimal parameters.

Key Words

System identification parameter constraints one-sided Gâteaux differentiable functionals distributed-parameter systems maximum principle 

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • W. H. Yu
    • 1
  1. 1.Department of MathematicsTianjin UniversityTianjinPeople's Republic of China

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