Asymptotic models for the discrete optimal control of the deformation of an elastic membrane

I. I. Argatov

Makarov State Naval Academy, St. Petersburg, 199026

Abstract: This paper considers the singularly perturbed static problem of the optimal control of the deformation of an elastic membrane by means of external loads (control without constraints) applied to several small areas distant from each other. The objective functional is equal to the sum of the square of the root-mean-square approximation error and the square of the norm of the external load. Asymptotic models are constructed using the method of matched asymptotic expansions.

Keywords: elastic membrane, control of quasipoint loads, asymptotic models.

UDC: 519.6

Received: 20.07.2004

 English version: Journal of Applied Mechanics and Technical Physics, 2006, 47:5, 724–735

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