No 4 (2018)
TO OPTIMALITY OF QUASI-SINGULAR CONTROL IN VARIABLE STRUCTURE CONTROL PROBLEM
Abstract
In the proposed paper, we study one composite optimal control problem described by a set of ordinary differential and integral equations. Admissible controls are selected from the class of piecewise-continuous functions. First, the calculated formula for the increment of the second-order quality functional. Then, assuming that the control domain is convex, a necessary first-order optimality condition is proved in the form of a linearized maximum condition. The case of degeneration of the linearized maximum condition (quasi-special case) is considered. The necessary conditions for optimality of quasi-singular controls are established. In the particular case, from the necessary optimality condition of the second order an analogue of the Legendre - Klebsch condition is obtained.
Applied Mathematics and Control Sciences. 2018;(4):7-30
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TO THE OPTIMALITY OF QUASI-SINGULAR CONTROL IN A DISCRETE STEPPED CONTROL PROBLEM WITH NONLOCAL BOUNDARY CONDITIONS
Abstract
Consider one step discrete optimal control problem described by a system of nonlinear difference equations with nonlocal boundary conditions. Under the assumption of convexity of control domains, an analogue of the linearized maximum condition is proved. The case of degeneracy of the linearized maximum condition has been specially studied.
Applied Mathematics and Control Sciences. 2018;(4):31-52
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ABSOLUTE STABILITY CONDITIONS FOR DIFFERENTIAL EQUATIONS WITH DISTRIBUTED DELAY
Abstract
The problem of asymptotic stability for autonomous functional differential equations is studied on the basis of the investigation of the roots of the characteristic function. We apply D -decomposition method for obtaining the sharp boundaries of stability domains. We obtain necessary and sufficient conditions of asymptotic stability for two families of linear autonomous differential equations with distributed delay and power kernels. These criteria of stability are formulated in terms of the parameters of the original problem. Based on the criteria, we find absolute stability conditions for each of the families.
Applied Mathematics and Control Sciences. 2018;(4):53-69
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MODELING THREE-INERT OSCILLATOR
Abstract
We consider a system with uniform oscillatory elements, namely, three massive loads (three-inert system). The possibility of occurrence of such a system free of harmonic oscillations which, as in the conventional oscillatory systems is caused by that its elements are different character reactivity. The oscillating system with three homogeneous (inert) components different reactivity is achieved by summing the spatial shift (2p/3) and phase shift (2p/3). The three-inert oscillator there is a mutual exchange between the kinetic energies of loads. Unlike traditional vibration systems free vibration frequency oscillatory systems with homogeneous elements do not depend on the system parameters and determined solely by the initial conditions, so that they can make available to any harmonic oscillations initially set frequency.
Applied Mathematics and Control Sciences. 2018;(4):73-79
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VECTORIZATION OF RASTER IMAGES
Abstract
This work is devoted to the development of program tools for vectorization of color bitmaps. The aim of the work is to develop an application for the translation of color raster graphics into vector format. The algorithm for vectorization of raster images Potrace is described, provides descriptions of vector formats Scalable Vector Graphics (SVG), Vector Markup Language (VML), Postscript, Adobe Portable Document Format (PDF), Adobe Illustrator.
Applied Mathematics and Control Sciences. 2018;(4):83-98
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ARTIFICIAL INTELLIGENCE IN PERM UNIVERSITIES: HISTORY AND SCIENTIFIC PRIORITY (REVIEW ARTICLE)
Abstract
The article is based on the annual Perm All-Russian scientific and practical conference "Artificial intelligence in solving urgent social and economic problems of the XXI century" (http://www.permai.ru/files/26.05.2018.pdf). It is also a brief overview of the results of the Perm branch of the Scientific Council of the Russian Academy of Sciences on the methodology of artificial intelligence, as well as several departments of the Perm state University, Perm state humanitarian pedagogical University, National research University Higher school of Economics, Perm state medical University. The review covers the works that develop and apply the methods of artificial intelligence in the classical sense, i.e., those methods that simulate human intellectual activity by simulating natural mechanisms. These are expert systems, genetic algorithms, neural networks, fuzzy mathematics. The scientific priority of Perm scientists in the development of theoretical foundations and practical applications of artificial intelligence is emphasized.
Applied Mathematics and Control Sciences. 2018;(4):99-130
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