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Siberian Mathematical Journal

, Volume 44, Issue 4, pp 695–712 | Cite as

Approximation of Attainable Sets of an Evolution Inclusion of Subdifferential Type

  • A. A. Tolstonogov
Article

Abstract

In a separable Hilbert space we consider an evolution inclusion with a multivalued perturbation and evolution operators that are subdifferentials of a proper convex lower semicontinuous function depending on time. Along with the original inclusion, we consider a sequence of approximating evolution inclusions with the same perturbation and the evolution operators that are subdifferentials of the Moreau–Yosida regularizations of the original function. We show that the attainable set of the original inclusion, regarded as a multivalued function of time, is the uniform (in time) limit in the Hausdorff metric of the sequence of attainable sets of the approximating inclusions. As an application we consider an example of a control system with discontinuous nonlinearity.

subdifferential Moreau–Yosida regularization continuous selection extreme point attainable set discontinuous nonlinearity 

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • A. A. Tolstonogov
    • 1
  1. 1.Institute of System Dynamics and Control TheoryIrkutsk

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