Continuous dependence on the data in abstract control problems

  • R. Lucchetti
  • F. Mignanego
Contributed Papers

Abstract

We consider the following problems: minimize
$$I_n (u) = |u - \hat u|^p + |L_n u - \hat y|^p , n \geqslant 0,$$
whereLn are equibounded linear operators. If we callun,u0 the minimum points ofIn, we characterize the strong convergence ofun tou0 in terms of the pointwise convergence ofLn and their adjoint operatorsLn* toL0 andL0*, respectively. Then, we apply this result to the case of a problem governed by a linear differential equation. Finally, we conclude by studying perturbations of an abstract constrained minimum problem.

Key Words

Perturbations of control problems duality theory E-spaces aligned elements 

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Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • R. Lucchetti
    • 1
  • F. Mignanego
    • 1
  1. 1.Institute of Mathematics, Faculty of SciencesUniversity of GenovaGenovaItaly

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