Asymptotics of Solutions of Periodic Problem for Generalized Nonlinear Hamiltonian System Singularly Perturbed by a Matrix

  • Authors:

  • Galina A. Kurina

  • Affiliations:

  • Voronezh State Forestry Academy, Voronezh, Russia

  • Venue:
  • Journal of Dynamical and Control Systems
  • Year:
  • 2008

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Abstract

The paper deals with the periodic problem for a generalized nonlinear Hamiltonian system, which appears from the control optimality condition for the periodic problem of the minimization of the functional on trajectories of the equation with the operator A驴+驴驴B standing before the derivative, where the operator A is singular and A驴+驴驴B is invertible for sufficiently small 驴驴驴0. Under some conditions, the asymptotic solution of such problem has been constructed in the form of the series with respect to nonnegative integer powers of 驴. The solvability of the considered problem has also been established for sufficiently small 驴驴驴0.