Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta最新文献

Coalitional Pareto optimal solution of one differential game 一个差分博弈的联盟帕累托最优解

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2024-05-01 DOI: 10.35634/2226-3594-2024-63-02

V.I. Zhukovskiy, L.V. Zhukovskaya, S.N. Sachkov, E.N. Sachkova

引用次数: 0

Integration of negative-order modified Korteweg–de Vries equation with an integral source 带积分源的负阶修正 Korteweg-de Vries 方程积分法

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2024-05-01 DOI: 10.35634/2226-3594-2024-63-06

G. Urazboev, M. M. Khasanov, O.B. Ismoilov

引用次数: 0

On the issue of control of neutral-type systems by hybrid controllers with state feedback 带状态反馈的混合控制器对中性型系统的控制问题

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2024-05-01 DOI: 10.35634/2226-3594-2024-63-07

V. E. Khartovskii

{"title":"On the issue of control of neutral-type systems by hybrid controllers with state feedback","authors":"V. E. Khartovskii","doi":"10.35634/2226-3594-2024-63-07","DOIUrl":"https://doi.org/10.35634/2226-3594-2024-63-07","url":null,"abstract":"For linear autonomous systems of neutral type, an approach to control design problems in the form of feedback based on a new class of hybrid controllers is proposed. The structure of hybrid regulators necessarily includes a differential equation, so the closed system becomes differential-algebraic. A distinctive feature of hybrid controllers is the existence of elementary transformation of equations of a closed-loop system, which make it possible to obtain an independent subsystem of neutral type. In this case, the specified subsystem of neutral type uniquely determines the behavior of the solution $x(t)$ of the original open-loop system (possibly as a vector component of the solution vector of the closed-loop system). The main advantages of using hybrid controllers include the possibility of their application to systems that do not satisfy the “traditional” controllability properties. The properties of hybrid controllers have been studied. The author gives an example of using these controllers to solve a new problem of controlling the coefficients of a characteristic quasi-polynomial in the case where the approaches known in the literature are not applicable. The possibility of using hybrid controllers to solve the $0$-controllability problem using the finite control method is demonstrated.","PeriodicalId":514517,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta","volume":"77 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141057216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Comparison theorem for systems of differential equations and its application to estimate the average time benefit from resource collection 微分方程系统的比较定理及其在估算资源收集的平均时间收益中的应用

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2024-05-01 DOI: 10.35634/2226-3594-2024-63-01

A. A. Bazulkina, L. I. Rodina

{"title":"Comparison theorem for systems of differential equations and its application to estimate the average time benefit from resource collection","authors":"A. A. Bazulkina, L. I. Rodina","doi":"10.35634/2226-3594-2024-63-01","DOIUrl":"https://doi.org/10.35634/2226-3594-2024-63-01","url":null,"abstract":"One of the versions of the comparison theorem for systems of ordinary differential equations is proved, the consequence of which is the property of monotonicity of solutions with respect to initial data. We consider the problem of estimating the average time profit from resource extraction for a structured population consisting of individual species $x_1,ldots,x_n$, or divided into $n$ age groups. We assume that the dynamics of the population in the absence of exploitation is given by a system of differential equations $dot x =f(x)$, and at times $tau(k)=kd$, $d>0$, a certain share of the biological resource is extracted from the population $u(k)=(u_1(k),ldots,u_n(k))in [0,1]^n$, $k=1,2,ldots.$ It is shown that using the comparison theorem it is possible to find estimates of the average time benefit in cases when analytical solutions for relevant systems are not known. The results obtained are illustrated for models of interaction between two species, such as symbiosis and competition. It is shown that for models of symbiosis, commensalism and neutralism, the greatest value of the average time profit is achieved with the simultaneous exploitation of two types of resources. For populations between which an interaction of the “competition” type is observed, cases in which it is advisable to extract only one type of resource are highlighted.","PeriodicalId":514517,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta","volume":"41 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141036785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On smoothness conditions and selection of the edge of a scattering surface in one class of 3D time-optimal problems 论一类三维时间最优问题中散射面边缘的平滑条件和选择

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2024-05-01 DOI: 10.35634/2226-3594-2024-63-03

P. D. Lebedev, A. A. Uspenskii

引用次数: 0

Double capture of coordinated evaders in recurrent differential games 重复性差分博弈中协调逃避者的双重捕获

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2024-05-01 DOI: 10.35634/2226-3594-2024-63-04

N.N. Petrov

引用次数: 0

On application of Gaussian kernels and Laplace functions combined with Kolmogorov's theorem for approximation of functions of several variables 关于高斯核和拉普拉斯函数与科尔莫戈罗夫定理相结合在多变量函数近似中的应用

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2024-05-01 DOI: 10.35634/2226-3594-2024-63-08

A.V. Chernov

{"title":"On application of Gaussian kernels and Laplace functions combined with Kolmogorov's theorem for approximation of functions of several variables","authors":"A.V. Chernov","doi":"10.35634/2226-3594-2024-63-08","DOIUrl":"https://doi.org/10.35634/2226-3594-2024-63-08","url":null,"abstract":"A special class of approximations of measurable functions of several variables on the unit coordinate cube is investigated. The class is constructed on the base of Kolmogorov's theorem (in version by Sprecher–Golubkov) stating that a continuous function $f$ of several variables can be represented as a finite superposition of continuous single-variable functions — so called outer functions (which depend of $f$) and inner one $Psi$ (which is independent of $f$ and is monotone). In the case of continuous functions $f$ the class under study is obtained with outer functions approximated by linear combinations of quadratic exponentials (also known as Gaussian functions or Gaussian kernels) and with the inner function $Psi$ approximated by Laplace functions. As is known, a measurable function $f$ can be approximated by a continuous one (up to a set of small measure) with the help of classical Luzin's theorem. The effectiveness of such approach is based on assertions that, firstly, the Mexican hat mother wavelet on any fixed bounded interval can be approximated as accurately as desired by a linear combination of two Gaussian functions, and, secondly, that a continuous monotone function on such an interval can be approximated as accurately as desired by a linear combination of translations and dilations of the Laplace integral (in other words, Laplace functions). It is proved that the class of approximations under study is dense everywhere in the class of continuous multivariable functions on the coordinate cube. For the case of continuous and piecewise continuous functions of two variables, numerical results are presented that confirm the effectiveness of approximations of the studied class.","PeriodicalId":514517,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta","volume":"29 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141045058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Set-valued mappings: fixed point results with $beta$-function and some applications 定值映射：$beta$函数的定点结果及一些应用

Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta Pub Date : 2024-05-01 DOI: 10.35634/2226-3594-2024-63-05

Y. Touail

引用次数: 0