ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

17. Control Theory and Optimization

1991 MS Classification: 34,49 Hildebrand, Roland, Moscow State University, Russia Optimal synthesis of controlled systems near a focus Consider a twodimensional controlled system

˙X⃗ = F⃗ + G⃗u, u ∈ [0, 1], I = ∫_{0}^{∞} C(X⃗) dt → min

where X⃗ ∈ R^{2}, 0 is a focus of the system ˙ X⃗ = F⃗, G⃗ is non-vanishing vector field, u is control. F⃗ , G⃗, C are three times continuously differentiable in a neighbourhood of 0, C begins with quadratic terms. Necessary and satisfying conditions on F⃗ , G⃗, C for existence of optimal synthesis are given in the general case. The optimal synthesis is described if exists.