In this article, we introduce fuzzy paratopological group, fuzzy semitopological group and fuzzy quasitopological group with illustrative examples and properties. These new notions belong to fuzzy topological group. Here, we prove that each fuzzy regular paratopological group is completely regular by using fuzzy uniformities. Moreover, we prove some results related to fuzzy semitopological group and fuzzy quasitopological group. In addition, we provide an application in the area of decision making during robot crash by using our above stated notions and nano topology.
{"title":"On fuzzy paratopological group and decision making during robot crash","authors":"A. Muneesh Kumar, P. Gnanachandra, S. Acharjee","doi":"10.35634/vm230205","DOIUrl":"https://doi.org/10.35634/vm230205","url":null,"abstract":"In this article, we introduce fuzzy paratopological group, fuzzy semitopological group and fuzzy quasitopological group with illustrative examples and properties. These new notions belong to fuzzy topological group. Here, we prove that each fuzzy regular paratopological group is completely regular by using fuzzy uniformities. Moreover, we prove some results related to fuzzy semitopological group and fuzzy quasitopological group. In addition, we provide an application in the area of decision making during robot crash by using our above stated notions and nano topology.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73421044","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}
In game theory and operations research theory, a minimax often appears for a function $f(x,y)$ that depends on two vector variables $x$, $y$. Many works have been devoted to the study of the properties of minimax (or maximin). A minimax can be interpreted as the smallest guaranteed result for the minimizing player (the minimizing operator). In the study of minimax problems, various correctness issues are of some interest. This paper is devoted to one of these issues. In it, vectors $x$, $y$ belong to compacts $P$, $Q$ of corresponding Euclidean spaces $R^k$, $R^l$, and function $f(x,y)$ is continuous on product of spaces $R^ktimes R^l$. The paper considers the dependence of minimax on small changes of compacts $P$, $Q$ in the Hausdorff metric. The continuity of the dependence of minimax on small variations of compacts $P$, $Q$ is proved.
{"title":"On one correctness problem for minimax","authors":"M. S. Nikol’skii","doi":"10.35634/vm230206","DOIUrl":"https://doi.org/10.35634/vm230206","url":null,"abstract":"In game theory and operations research theory, a minimax often appears for a function $f(x,y)$ that depends on two vector variables $x$, $y$. Many works have been devoted to the study of the properties of minimax (or maximin). A minimax can be interpreted as the smallest guaranteed result for the minimizing player (the minimizing operator). In the study of minimax problems, various correctness issues are of some interest. This paper is devoted to one of these issues. In it, vectors $x$, $y$ belong to compacts $P$, $Q$ of corresponding Euclidean spaces $R^k$, $R^l$, and function $f(x,y)$ is continuous on product of spaces $R^ktimes R^l$. The paper considers the dependence of minimax on small changes of compacts $P$, $Q$ in the Hausdorff metric. The continuity of the dependence of minimax on small variations of compacts $P$, $Q$ is proved.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84789812","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}
Let $T_{rho}$ be an irrational rotation on a unit circle $S^{1}simeq [0,1)$. Consider the sequence ${mathcal{P}_{n}}$ of increasing partitions on $S^{1}$. Define the hitting times $N_{n}(mathcal{P}_n;x,y):= inf{jgeq 1mid T^{j}_{rho}(y)in P_{n}(x)}$, where $P_{n}(x)$ is an element of $mathcal{P}_{n}$ containing $x$. D. Kim and B. Seo in [9] proved that the rescaled hitting times $K_n(mathcal{Q}_n;x,y):= frac{log N_n(mathcal{Q}_n;x,y)}{n}$ a.e. (with respect to the Lebesgue measure) converge to $log2$, where the sequence of partitions ${mathcal{Q}_n}$ is associated with chaotic map $f_{2}(x):=2x bmod 1$. The map $f_{2}(x)$ has positive entropy $log2$. A natural question is what if the sequence of partitions ${mathcal{P}_n}$ is associated with a map with zero entropy. In present work we study the behavior of $K_n(tau_n;x,y)$ with the sequence of mixed partitions ${tau_{n}}$ such that $ mathcal{P}_{n}cap [0,frac{1}{2}]$ is associated with map $f_{2}$ and $mathcal{D}_{n}cap [frac{1}{2},1]$ is associated with irrational rotation $T_{rho}$. It is proved that $K_n(tau_n;x,y)$ a.e. converges to a piecewise constant function with two values. Also, it is shown that there are some irrational rotations that exhibit different behavior.
{"title":"Hitting functions for mixed partitions","authors":"A. Dzhalilov, M. Khomidov","doi":"10.35634/vm230201","DOIUrl":"https://doi.org/10.35634/vm230201","url":null,"abstract":"Let $T_{rho}$ be an irrational rotation on a unit circle $S^{1}simeq [0,1)$. Consider the sequence ${mathcal{P}_{n}}$ of increasing partitions on $S^{1}$. Define the hitting times $N_{n}(mathcal{P}_n;x,y):= inf{jgeq 1mid T^{j}_{rho}(y)in P_{n}(x)}$, where $P_{n}(x)$ is an element of $mathcal{P}_{n}$ containing $x$. D. Kim and B. Seo in [9] proved that the rescaled hitting times $K_n(mathcal{Q}_n;x,y):= frac{log N_n(mathcal{Q}_n;x,y)}{n}$ a.e. (with respect to the Lebesgue measure) converge to $log2$, where the sequence of partitions ${mathcal{Q}_n}$ is associated with chaotic map $f_{2}(x):=2x bmod 1$. The map $f_{2}(x)$ has positive entropy $log2$. A natural question is what if the sequence of partitions ${mathcal{P}_n}$ is associated with a map with zero entropy. In present work we study the behavior of $K_n(tau_n;x,y)$ with the sequence of mixed partitions ${tau_{n}}$ such that $ mathcal{P}_{n}cap [0,frac{1}{2}]$ is associated with map $f_{2}$ and $mathcal{D}_{n}cap [frac{1}{2},1]$ is associated with irrational rotation $T_{rho}$. It is proved that $K_n(tau_n;x,y)$ a.e. converges to a piecewise constant function with two values. Also, it is shown that there are some irrational rotations that exhibit different behavior.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90860194","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}
It is well known that conjugate gradient methods are useful for solving large-scale unconstrained nonlinear optimization problems. In this paper, we consider combining the best features of two conjugate gradient methods. In particular, we give a new conjugate gradient method, based on the hybridization of the useful DY (Dai-Yuan), and HZ (Hager-Zhang) methods. The hybrid parameters are chosen such that the proposed method satisfies the conjugacy and sufficient descent conditions. It is shown that the new method maintains the global convergence property of the above two methods. The numerical results are described for a set of standard test problems. It is shown that the performance of the proposed method is better than that of the DY and HZ methods in most cases.
{"title":"A new hybrid conjugate gradient algorithm for unconstrained optimization","authors":"I. Hafaidia, H. Guebbai, M. Al-Baali, M. Ghiat","doi":"10.35634/vm230211","DOIUrl":"https://doi.org/10.35634/vm230211","url":null,"abstract":"It is well known that conjugate gradient methods are useful for solving large-scale unconstrained nonlinear optimization problems. In this paper, we consider combining the best features of two conjugate gradient methods. In particular, we give a new conjugate gradient method, based on the hybridization of the useful DY (Dai-Yuan), and HZ (Hager-Zhang) methods. The hybrid parameters are chosen such that the proposed method satisfies the conjugacy and sufficient descent conditions. It is shown that the new method maintains the global convergence property of the above two methods. The numerical results are described for a set of standard test problems. It is shown that the performance of the proposed method is better than that of the DY and HZ methods in most cases.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72733180","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}
In a finite-dimensional Euclidean space, the problem of pursuit of two evaders by a group of pursuers described by a system of the form $$ dot z_{ij} = u_i - v,quad u_i,v in V, $$ is considered. It is assumed that all evaders use the same control. The pursuers use counterstrategies based on information about the initial positions and control history of the evaders. The set of admissible controls $V$ is a unit ball centered at zero, target sets are the origin of coordinates. The goal of the pursuers' group is to capture at least one evader by two pursuers. In terms of initial positions and game parameters a sufficient condition for the capture is obtained. In the study, the method of resolving functions is used as a basic one, which allows obtaining sufficient conditions for the solvability of the approach problem in some guaranteed time.
在有限维欧几里得空间中，考虑了由$$dot z_{ij} = u_i - v,quad u_i,v in V, $$形式的系统描述的一组追赶者对两个逃避者的追赶问题。假设所有逃避者使用相同的控制。追捕者根据关于逃避者的初始位置和控制历史的信息使用对抗策略。容许控制的集合$V$是一个以0为中心的单位球，目标集合是坐标的原点。追捕者组的目标是用两名追捕者捕获至少一名逃跑者。在初始位置和博弈参数方面，得到了捕获的充分条件。在本研究中，采用函数解析法作为基本方法，可以在一定保证时间内得到逼近问题可解的充分条件。
{"title":"Two-time capture of coordinated evaders in a simple pursuit problem","authors":"N. Petrov","doi":"10.35634/vm230207","DOIUrl":"https://doi.org/10.35634/vm230207","url":null,"abstract":"In a finite-dimensional Euclidean space, the problem of pursuit of two evaders by a group of pursuers described by a system of the form\u0000$$\u0000dot z_{ij} = u_i - v,quad u_i,v in V, \u0000$$\u0000is considered. It is assumed that all evaders use the same control. The pursuers use counterstrategies based on information about the initial positions and control history of the evaders. The set of admissible controls $V$ is a unit ball centered at zero, target sets are the origin of coordinates. The goal of the pursuers' group is to capture at least one evader by two pursuers. In terms of initial positions and game parameters a sufficient condition for the capture is obtained. In the study, the method of resolving functions is used as a basic one, which allows obtaining sufficient conditions for the solvability of the approach problem in some guaranteed time.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72476871","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}
One of the versions of the generalized variational Ginzburg-Landau equation is considered, supplemented by periodic boundary conditions. For such a boundary value problem, the question of existence, stability, and local bifurcations of single-mode equilibrium states is studied. It is shown that in the case of a nearly critical threefold zero eigenvalue, in the problem of stability of single-mode spatially inhomogeneous equilibrium states, subcritical bifurcations of two-dimensional invariant tori filled with spatially inhomogeneous equilibrium states are realized. The analysis of the stated problem is based on such methods of the theory of infinite-dimensional dynamical systems as the theory of invariant manifolds and the apparatus of normal forms. Asymptotic formulas are obtained for the solutions that form invariant tori.
{"title":"Stability and local bifurcations of single-mode equilibrium states of the Ginzburg-Landau variational equation","authors":"D. A. Kulikov","doi":"10.35634/vm230204","DOIUrl":"https://doi.org/10.35634/vm230204","url":null,"abstract":"One of the versions of the generalized variational Ginzburg-Landau equation is considered, supplemented by periodic boundary conditions. For such a boundary value problem, the question of existence, stability, and local bifurcations of single-mode equilibrium states is studied. It is shown that in the case of a nearly critical threefold zero eigenvalue, in the problem of stability of single-mode spatially inhomogeneous equilibrium states, subcritical bifurcations of two-dimensional invariant tori filled with spatially inhomogeneous equilibrium states are realized.\u0000The analysis of the stated problem is based on such methods of the theory of infinite-dimensional dynamical systems as the theory of invariant manifolds and the apparatus of normal forms. Asymptotic formulas are obtained for the solutions that form invariant tori.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81698583","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}
Nonstationary motion of a liquid binary mixture in a narrow long horizontal channel with rigid walls heated according to a certain law is considered. The possibility of applying the Ostroumov-Birikh solution to the description of the flow under study is used. It reduces the problem to solving a mixed boundary value problem for a system of parabolic equations. A feature of the problem is an additional integral condition on the fluid flow rate. It allows finding the pressure gradient together with the functions of velocity, temperature, and concentration. Applying the constructed numerical procedure, the analysis of the obtained characteristics of motion is carried out using water-ethanol solution as a mixture. The possibilities of stabilizing the unsteady flow and controlling the motion by means of a periodically changing thermal load on the channel wall are shown.
{"title":"Numerical solution of nonstationary problem for convection of binary mixture in horizontal layer","authors":"I. Stepanova, V. Zalizniak","doi":"10.35634/vm230212","DOIUrl":"https://doi.org/10.35634/vm230212","url":null,"abstract":"Nonstationary motion of a liquid binary mixture in a narrow long horizontal channel with rigid walls heated according to a certain law is considered. The possibility of applying the Ostroumov-Birikh solution to the description of the flow under study is used. It reduces the problem to solving a mixed boundary value problem for a system of parabolic equations. A feature of the problem is an additional integral condition on the fluid flow rate. It allows finding the pressure gradient together with the functions of velocity, temperature, and concentration. Applying the constructed numerical procedure, the analysis of the obtained characteristics of motion is carried out using water-ethanol solution as a mixture. The possibilities of stabilizing the unsteady flow and controlling the motion by means of a periodically changing thermal load on the channel wall are shown.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72877955","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}
In the article, a nonlocal boundary value problem has been investigated for a fourth-order mixed-type equation degenerating inside and on the boundary of a domain. Applying the method of separation of variables to the problem under study, the spectral problem for an ordinary differential equation is obtained. The Green function of the last problem is constructed, with the help of which it is equivalently reduced to the Fredholm integral equation of the second kind with a symmetric kernel, which implies the existence of eigenvalues and the system of eigenfunctions for the spectral problem. The theorem of expansion of a given function into a uniformly convergent series with respect to the system of eigenfunctions is proved. Using the found integral equation and Mercer's theorem, a uniform convergence of some bilinear series depending on the found eigenfunctions is proved. The order of the Fourier coefficients is established. The solution of the problem under study is written as the sum of the Fourier series with respect to the system of eigenfunctions of the spectral problem. An estimate for the problem's solution is obtained, from which its continuous dependence on the given functions follows.
{"title":"On one problem for a fourth-order mixed-type equation that degenerates inside and on the boundary of a domain","authors":"A. Urinov, D. A. Usmonov","doi":"10.35634/vm230209","DOIUrl":"https://doi.org/10.35634/vm230209","url":null,"abstract":"In the article, a nonlocal boundary value problem has been investigated for a fourth-order mixed-type equation degenerating inside and on the boundary of a domain. Applying the method of separation of variables to the problem under study, the spectral problem for an ordinary differential equation is obtained. The Green function of the last problem is constructed, with the help of which it is equivalently reduced to the Fredholm integral equation of the second kind with a symmetric kernel, which implies the existence of eigenvalues and the system of eigenfunctions for the spectral problem. The theorem of expansion of a given function into a uniformly convergent series with respect to the system of eigenfunctions is proved. Using the found integral equation and Mercer's theorem, a uniform convergence of some bilinear series depending on the found eigenfunctions is proved. The order of the Fourier coefficients is established. The solution of the problem under study is written as the sum of the Fourier series with respect to the system of eigenfunctions of the spectral problem. An estimate for the problem's solution is obtained, from which its continuous dependence on the given functions follows.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78555795","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}
We study a multidimensional case of a nonlinear reaction-diffusion system modeled by a system of two parabolic equations with power nonlinearities. Such systems can be used to simulate the process of propagation in space of interacting distributed formations of robots of two types. Such equations also describe the processes of nonlinear diffusion in reacting two-component continuous media. An original version of the reduction method is proposed, which reduces the construction of the dependence of the exact solution on spatial variables to the solution of the Helmholtz equation, and the dependence on time to the solution of a linear system of ordinary differential equations. A number of examples of multiparameter families of exact solutions given by elementary functions are constructed.
{"title":"On multidimensional exact solutions of a nonlinear reaction-diffusion system","authors":"A. A. Kosov, E. Semenov, V. V. Tirskikh","doi":"10.35634/vm230203","DOIUrl":"https://doi.org/10.35634/vm230203","url":null,"abstract":"We study a multidimensional case of a nonlinear reaction-diffusion system modeled by a system of two parabolic equations with power nonlinearities. Such systems can be used to simulate the process of propagation in space of interacting distributed formations of robots of two types. Such equations also describe the processes of nonlinear diffusion in reacting two-component continuous media. An original version of the reduction method is proposed, which reduces the construction of the dependence of the exact solution on spatial variables to the solution of the Helmholtz equation, and the dependence on time to the solution of a linear system of ordinary differential equations. A number of examples of multiparameter families of exact solutions given by elementary functions are constructed.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80549458","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}
In the article, a problem of solution estimation for linear autonomous completely regular differential-algebraic systems with many commensurate delays is investigated. The class of completely regular differential-algebraic systems with delay under study includes the classes of linear systems of delayed and neutral types; in addition, the analysis of continuous-discrete systems is reduced to completely regular systems. For linear autonomous completely regular differential-algebraic systems with many commensurate delays, the property of asymptotic observability is determined, which are characterized by the fact that all solutions generating the same output signal are indistinguishable in the future. Conditions for asymptotic observability expressed in terms of the parameters of the original system are formulated and proved. For asymptotically observable systems, a solution estimation procedure is proposed, the implementation of which consists of the following steps. First, using the observed output, a linear autonomous non-homogeneous asymptotically observable retarded type system with a non-homogeneous part depending on the output is put in correspondence with the original system. The solution of the new system uniquely determines the solution of the original system. Then a transformation is constructed that reduces the matrices of the retarded type system to a certain form. After that, with the help of a finite chain of observers, the solution is evaluated. The results of the presented study are applicable to systems that do not have the property of final observability, which makes it possible to significantly reduce the requirements for observing organs when modeling the corresponding objects of the real world.
{"title":"Estimation of the solution of asymptotically observable linear completely regular differential-algebraic systems with delay","authors":"V. E. Khartovskii","doi":"10.35634/vm230210","DOIUrl":"https://doi.org/10.35634/vm230210","url":null,"abstract":"In the article, a problem of solution estimation for linear autonomous completely regular differential-algebraic systems with many commensurate delays is investigated. The class of completely regular differential-algebraic systems with delay under study includes the classes of linear systems of delayed and neutral types; in addition, the analysis of continuous-discrete systems is reduced to completely regular systems.\u0000For linear autonomous completely regular differential-algebraic systems with many commensurate delays, the property of asymptotic observability is determined, which are characterized by the fact that all solutions generating the same output signal are indistinguishable in the future. Conditions for asymptotic observability expressed in terms of the parameters of the original system are formulated and proved. For asymptotically observable systems, a solution estimation procedure is proposed, the implementation of which consists of the following steps. First, using the observed output, a linear autonomous non-homogeneous asymptotically observable retarded type system with a non-homogeneous part depending on the output is put in correspondence with the original system. The solution of the new system uniquely determines the solution of the original system. Then a transformation is constructed that reduces the matrices of the retarded type system to a certain form. After that, with the help of a finite chain of observers, the solution is evaluated. The results of the presented study are applicable to systems that do not have the property of final observability, which makes it possible to significantly reduce the requirements for observing organs when modeling the corresponding objects of the real world.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78127103","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}
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