Methods for Optimal Control and Control Theory

Article # 29_2017

37 p.

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Aleksander Stolbov
Software for complex studies of social-ecological and economic systems based on Region models: an analytical review

The article presents a historical overview and current state in the development of software that supports the research of social ecological and economic systems based on the “Region” models. The review covers development from the mid-1970s to the present.
The analysis of publications, reports and, where it was possible, documentation was carried out. The architecture of software systems, their main features and implementation methods were considered and analyzed. To represent some aspects of software, UML diagrams are exploited. The main purposes of considered software systems are the following: calculation experiment and scenario analysis, solving optimization and normalization problems, analyzing model properties and identifying parameters. The classification and comparison of software were carried out, then conclusions are drawn and future works delineated. (In Russian).

Key words: software, social ecological economical systems, analytical review.

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Article # 34_2017

14 p.

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V. Markasheva, A. Mashtakov
Existence of Global Fundamental Solution to a Class of Fokker–Planck Equations

In this paper, we investigate global solvability of the Fokker–Planck equations of a special type. Such equations arise in models of the primary visual cortex of the human brain and describe a process of anisotropic blurring of the image of the visual field on the retina of the eye. By modifying the Folland lifting technique for linear hypoelliptic differential operators satisfying the Hormander condition, we propose a method to saturate the system of vector fields in the equation to a basis of the tangent space at every point. We present the conditions that guarantee existence of a global fundamental solution to the considered equations.

Key words: nilpotent and stratified Lie groups, lifting of operator, saturation, fundamental solution.

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Article # 37_2017

17 p.

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Elena Sachkova
Nondegenerate abnormal control in sub-riemannian problem with growth vector (2, 3, 5, 8)

Nilpotent sub-Riemannian problem with growth vector (2, 3, 5, 8) are considered. Canonical abnormal controls are described. Formulas for the corresponding conjugate vectors of the Pontryagin maximum principle are obtained. (In Russian).

Key words: sub-Riemannian problem, abnormal controls, abnormal trajectories.

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