FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 1, PAGES 199-233

Classification of phase portraits of optimal syntheses

R. Hildebrand

Abstract

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The paper is devoted to the investigation of controllable oscillating systems of ordinary differential equations affine in scalar nonsymmetric control in a neighborhood of a singular point of focus or center type. Integrands in value functionals are quadratic in phase coordinates. We classify such systems in case of general position by arising optimal syntheses. The existence of optimal synthesis is proved and its structure is described.

All articles are published in Russian.

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Last modified: May 10, 2001