Group specialties in the problem of the maximum principle for systems with deviating argument View Full Text


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Article Info

DATE

2012-07

AUTHORS

L. A. Beklaryan

ABSTRACT

The problem of equivalence of the maximum principle in strong pointwise and integral forms is investigated in an optimum control problem in which dynamics is described by a functional-differential equation of pointwise type (a differential equation with deviating argument). The maximum principle in the strong pointwise form is formulated in the aspect of a two-parametrical set of finite-dimensional extremal problems [1,2]. Like it is in ordinary systems, the first parameter is time t and the second parameter is a length of the words which are composed by the generators of finitely generated group Q of homeomorphisms of the real line and which are generated by the functions of a deviation of the argument (for the ordinary systems the corresponding group Q is trivial). The maximum principle in the strong pointwise form follows from the maximum principle in the integral form. The basic obstacle for the equivalence of two forms is a combinatorial condition on the group Q. The presence of noted combinatorial property involves the existence of metric invariants for the group Q that allows to describe its structure in more detail. More... »

PAGES

419-432

References to SciGraph publications

  • 1981-12. Groups of polynomial growth and expanding maps in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/s10883-012-9151-6

    DOI

    http://dx.doi.org/10.1007/s10883-012-9151-6

    DIMENSIONS

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