scholarly journals PARAMETRIC SYNTHESIS OF A MOVING OBJECT STABILIZER

2021 ◽  
pp. 10-19
Author(s):  
Yevgen Aleksandrov ◽  
Viktor Vanin ◽  
Tetyana Aleksandrova ◽  
Boris Vanin
Keyword(s):  
Global Minimum ◽  
Integral Functional ◽  
Small Neighborhood ◽  
Grid Method ◽  
Weight Coefficient ◽  
Dynamic Features ◽  
Parametric Synthesis ◽  
Variable Parameters ◽  
Object State ◽  
Working Point

The problem of choosing the variable parameters of a stabilizer of an object which minimize an additive quadratic integral functional reflecting the complex of requirements for a closed stabilization system is considered. To solve the problem a combined method of parametric synthesis of the stabilizer, which is a sequential combination of the Sobol grid method and the Nelder-Mead method, is proposed. At the first stage of the method by applying the Sobolev grid method a working point of the closed system in the pace of its variable parameters is transferred into a neighborhood of the quality functional global minimum point. Then at the second stage the Nelder-Mead method is used to relocated the working point into a small neighborhood of the global minimum. The method proposed comprises a particular algorithm for choosing the weight coefficient of the additive quality functional as well as makes use of the stabilization object state vector main coordinates, which provide the most adequate description of its dynamic features. The properties of a mathematical model of controlled system with discontinuous stabilization process control are studied numerically. The analysis of the plots in the dynamical system state phase space indicates non-spiral approach of the system to its equilibrium state. The synthesized control is realized in the form of a sequence of switchovers.

Parameter identification of discrete stochastic systems by the inverse iteration method

2020 ◽  
pp. 66-76
Author(s):  
Андрей Александрович Ломов
Keyword(s):  
Global Minimum ◽  
Stochastic Systems ◽  
Small Neighborhood ◽  
Small Radius ◽  
Large Radius ◽  
Matrix Elements ◽  
State Variables ◽  
True Value ◽  
High Convergence Rate ◽  
Equivalent Systems

Получены условия глобальной сходимости алгоритмов, основанных на обратных итерациях в переменной метрике, в задаче идентификации параметров дискретной стохастической системы с возмущениями в невязке уравнения и наблюдениях процессов. Доказана сходимость оценок параметров к истинному значению при увеличении объема выборки наблюдений истинного процесса. Приведены примеры расчетов The article addresses the problem of identifying parameters of discrete stochastic systems with perturbations in the residual of the equation and observation of variables. The identification functional in the problem has a complex nature of isosurfaces, which is why universal minimization algorithms based on estimates of the first and second derivatives have a small radius of convergence. It is proposed to employ efficient computational identification algorithms with inverse iterations in a variable metric for solving the convergence problem for two classes of systems with simple correspondence between matrix elements and parameters of equivalent systems without state variables. These algorithms are used for systems without state variables due to the large radius and high convergence rate since the 1970s. At first, a theorem on the conditions for convergence of inverse iterations from almost any initial approximation to a small neighborhood of the global minimum of the identification functional was proved. Secondly, a theorem on the convergence of the points of the global minimum of the identification functional to the desired true value with an increase in the sample size of observations is taken into account. Assumption of a zero first and restricted second moments of stochastic disturbances in the residual of the equation and observation of variables was made. The convergence of inverse iterations is shown numerically in a model example with significant values of disturbances. The result of the article is new theorems on the conditions of global convergence of computational algorithms with inverse iterations in the problem with mixed disturbances and the justification of possibility of using these algorithms to identify the parameters for discrete stochastic systems of two classes with a simple correspondence between matrix elements and parameters of equivalent systems without state variables

Properties of the beta coefficient of the global minimum variance portfolio

2020 ◽  
Vol 8 (1) ◽  
pp. 11-21
Author(s):  
S. M. Yaroshko ◽  
◽  
M. V. Zabolotskyy ◽  
T. M. Zabolotskyy ◽  
◽  
...  
Keyword(s):  
Confidence Interval ◽  
Asymptotic Distribution ◽  
Global Minimum ◽  
Asset Returns ◽  
Minimum Variance ◽  
Benchmark Portfolio ◽  
Beta Coefficient ◽  
Minimum Variance Portfolio ◽  
Global Minimum Variance Portfolio ◽  
Daily Returns

The paper is devoted to the investigation of statistical properties of the sample estimator of the beta coefficient in the case when the weights of benchmark portfolio are constant and for the target portfolio, the global minimum variance portfolio is taken. We provide the asymptotic distribution of the sample estimator of the beta coefficient assuming that the asset returns are multivariate normally distributed. Based on the asymptotic distribution we construct the confidence interval for the beta coefficient. We use the daily returns on the assets included in the DAX index for the period from 01.01.2018 to 30.09.2019 to compare empirical and asymptotic means, variances and densities of the standardized estimator for the beta coefficient. We obtain that the bias of the sample estimator converges to zero very slowly for a large number of assets in the portfolio. We present the adjusted estimator of the beta coefficient for which convergence of the empirical variances to the asymptotic ones is not significantly slower than for a sample estimator but the bias of the adjusted estimator is significantly smaller.

Continuity of homotopies

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Open Subset ◽  
Small Neighborhood ◽  
Unit Vector ◽  
Zariski Topology ◽  
Simple Point ◽  
Smooth Variety ◽  
Additional Material ◽  
Generic Type ◽  
Zariski Open Subset

This chapter includes some additional material on homotopies. In particular, for a smooth variety V, there exists an “inflation” homotopy, taking a simple point to the generic type of a small neighborhood of that point. This homotopy has an image that is properly a subset of unit vector V, and cannot be understood directly in terms of definable subsets of V. The image of this homotopy retraction has the merit of being contained in unit vector U for any dense Zariski open subset U of V. The chapter also proves the continuity of functions and homotopies using continuity criteria and constructs inflation homotopies before proving GAGA type results for connectedness. Additional results regarding the Zariski topology are given.

A Dynamic View of Global Integration and Local Responsiveness Framework

2018 ◽  
Vol 6 (8) ◽  
pp. 58
Author(s):  
Uyen-Minh Le ◽  
Tung-Shan Liao
Keyword(s):  
International Business ◽  
Business Management ◽  
External Environment ◽  
Dynamic Capability ◽  
International Strategy ◽  
Global Integration ◽  
Dynamic Features ◽  
Dynamic View ◽  
Concept Building ◽  
Strategy Types

Global-Integration and Local-Responsiveness (IR) framework with four pairs of external environment and appropriate international strategy types has contributed significantly to international business management. Nevertheless, the framework is still incomplete and lacks dynamic features. To deal with such limitations and enhance the theory, this paper, therefore, brings dynamic features regarding both environment and strategy into the IR grid. Under a dynamic capability angle with three steps of sensing, seizing and transforming [30], the dynamic global integration and local responsiveness framework – a new concept building for international business – would be explicated.

STRUCTURAL AND DYNAMIC FEATURES OF EAR-LY DISABILITY DUE TO MENTAL DISEASES

2020 ◽  
pp. 62-67
Author(s):  
Shmakova O.P.
Keyword(s):  
People With Disabilities ◽  
Child And Adolescent Psychiatry ◽  
Child Psychiatrist ◽  
Childhood And Adolescence ◽  
Disabled Children ◽  
Dynamic Features ◽  
Factors Affecting ◽  
Number Of Children ◽  
Number Of Patients

Prevention of disability is one of the most significant tasks of child and adolescent psychiatry. Obtaining data on the dynamics of the number of people with disabilities and the factors affecting this indicator seems to be one of the relevant aspects. Aim: to trace the dynamics of the number of children with disabili-ties and to assess the change in the structure of early disability over the past decades. Materials and Meth-ods. A comparative analysis of two cohorts of patients was carried out: 1st - patients born in 1990-1992. (1203 patients (men - 914, 76%; women - 289, 24%)) who applied to the district neuropsychiatric dispensa-ry for outpatient care in childhood and adolescence; II - children and adolescents born in 2005 - 2018 (602 patients (male - 410, 68%; female - 192, 32%), ob-served at the time of the study by a child psychiatrist in the neuropsychiatric dispensary. Research methods: clinical and psychopathological; follow-up; statisti-cal. Results. Comparison of the number and nosologi-cal distribution of disabled children in two cohorts showed that over the 15th year there has been a shift towards an increase in the proportion of disabled children among patients observed by child and ado-lescent psychiatrists. The increase in the number of children with disabilities was due to those suffering from childhood autism and other disorders of general development. There were no statistically significant differences in the number of people with disabilities who received benefits before the age of 7, as well as differences in gender ratios among disabled people in the two cohorts. Conclusion. Early disability is a mul-tifactorial phenomenon, prevalence, dynamics, the structure of which depends not only on clinical, but also on socio-administrative realities. Children with autism require increased attention, since there has been a multiple increase in the number of patients with this diagnosis.

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