Pub Date : 2022-05-01DOI: 10.35634/2226-3594-2022-59-02
M. Ait Hammou, E. Rami
We consider the $p(x)$-Laplacian equation with a Dirichlet boundary value condition $$ begin{cases} -Delta_{p(x)}(u)+|u|^{p(x)-2}u= g(x,u,nabla u), &xinOmega, u=0, &xinpartialOmega. end{cases} $$ Using the topological degree constructed by Berkovits, we prove, under appropriate assumptions, the existence of weak solutions for this equation.
{"title":"Existence of weak solutions for a $p(x)$-Laplacian equation via topological degree","authors":"M. Ait Hammou, E. Rami","doi":"10.35634/2226-3594-2022-59-02","DOIUrl":"https://doi.org/10.35634/2226-3594-2022-59-02","url":null,"abstract":"We consider the $p(x)$-Laplacian equation with a Dirichlet boundary value condition $$ begin{cases} -Delta_{p(x)}(u)+|u|^{p(x)-2}u= g(x,u,nabla u), &xinOmega, u=0, &xinpartialOmega. end{cases} $$ Using the topological degree constructed by Berkovits, we prove, under appropriate assumptions, the existence of weak solutions for this equation.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74153128","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}
Pub Date : 2022-05-01DOI: 10.35634/2226-3594-2022-59-03
V. Zhukovskiĭ, L. Zhukovskaya, S. P. Samsonov, L. Smirnova
In the middle of the last century the American mathematician and statistician professor of Michigan University Leonard Savage (1917-1971) and the well-known economist, professor of Zurich University (Switzerland) Jurg Niehans (1919-2007) independently from each other suggested the approach to decision-making in one-criterion problem under uncertainty (OPU), called the principle of minimax regret. This principle along with Wald principle of guaranteed result (maximin) is playing the most important role in guaranteed under uncertainty decision-making in OPU. The main role in the principle of minimax regret is carrying out the regret function, which determines the Niehans-Savage risk in OPU. Such risk has received the broad extension in practical problems during last years. In the present article we suggest one of possible approaches to finding decision in OPU from the position of a decision-maker, which simultaneously tries to increase the payoff (outcome) and to reduce the risk (i.e., “to kill two birds with one stone in one throw”). As an application, an explicit form of such a solution was immediately found for a linear-quadratic variant of the OPU of a fairly general form.
{"title":"The Savage principle and accounting for outcome in single-criterion nonlinear problem under uncertainty","authors":"V. Zhukovskiĭ, L. Zhukovskaya, S. P. Samsonov, L. Smirnova","doi":"10.35634/2226-3594-2022-59-03","DOIUrl":"https://doi.org/10.35634/2226-3594-2022-59-03","url":null,"abstract":"In the middle of the last century the American mathematician and statistician professor of Michigan University Leonard Savage (1917-1971) and the well-known economist, professor of Zurich University (Switzerland) Jurg Niehans (1919-2007) independently from each other suggested the approach to decision-making in one-criterion problem under uncertainty (OPU), called the principle of minimax regret. This principle along with Wald principle of guaranteed result (maximin) is playing the most important role in guaranteed under uncertainty decision-making in OPU. The main role in the principle of minimax regret is carrying out the regret function, which determines the Niehans-Savage risk in OPU. Such risk has received the broad extension in practical problems during last years. In the present article we suggest one of possible approaches to finding decision in OPU from the position of a decision-maker, which simultaneously tries to increase the payoff (outcome) and to reduce the risk (i.e., “to kill two birds with one stone in one throw”). As an application, an explicit form of such a solution was immediately found for a linear-quadratic variant of the OPU of a fairly general form.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91217652","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}
Pub Date : 2021-11-01DOI: 10.35634/2226-3594-2021-58-06
A. G. Chentsov, A. Chentsov, A. Sesekin
The problem of sequential bypass of megalopolises is investigated, focused on the problem of dismantling a system of radiation hazardous objects under constraints in the form of precedence conditions. The radiation impact on the performers is assessed by the doses received during movements and during the performance of dismantling works. The route problem of minimizing the dose load of workers carrying out dismantling in one or another sequence of operations is considered. The procedure for constructing an optimal solution using a variant of dynamic programming is investigated. On this basis, an algorithm is built, implemented on a PC. Examples of the numerical solution of a model problem for the minimum dose load are given.
{"title":"One task of routing jobs in high radiation conditions","authors":"A. G. Chentsov, A. Chentsov, A. Sesekin","doi":"10.35634/2226-3594-2021-58-06","DOIUrl":"https://doi.org/10.35634/2226-3594-2021-58-06","url":null,"abstract":"The problem of sequential bypass of megalopolises is investigated, focused on the problem of dismantling a system of radiation hazardous objects under constraints in the form of precedence conditions. The radiation impact on the performers is assessed by the doses received during movements and during the performance of dismantling works. The route problem of minimizing the dose load of workers carrying out dismantling in one or another sequence of operations is considered. The procedure for constructing an optimal solution using a variant of dynamic programming is investigated. On this basis, an algorithm is built, implemented on a PC. Examples of the numerical solution of a model problem for the minimum dose load are given.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85514465","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}
Pub Date : 2021-11-01DOI: 10.35634/2226-3594-2021-58-03
I. V. Izmestyev, V. I. Ukhobotov
In a normed space of finite dimension, a discrete game problem with fixed duration is considered. The terminal set is determined by the condition that the norm of the phase vector belongs to a segment with positive ends. In this paper, a set defined by this condition is called a ring. At each moment, the vectogram of the first player's controls is a certain ring. The controls of the second player at each moment are taken from balls with given radii. The goal of the first player is to lead a phase vector to the terminal set at a fixed time. The goal of the second player is the opposite. In this paper, necessary and sufficient termination conditions are found, and optimal controls of the players are constructed.
{"title":"On a discrete game problem with non-convex control vectograms","authors":"I. V. Izmestyev, V. I. Ukhobotov","doi":"10.35634/2226-3594-2021-58-03","DOIUrl":"https://doi.org/10.35634/2226-3594-2021-58-03","url":null,"abstract":"In a normed space of finite dimension, a discrete game problem with fixed duration is considered. The terminal set is determined by the condition that the norm of the phase vector belongs to a segment with positive ends. In this paper, a set defined by this condition is called a ring. At each moment, the vectogram of the first player's controls is a certain ring. The controls of the second player at each moment are taken from balls with given radii. The goal of the first player is to lead a phase vector to the terminal set at a fixed time. The goal of the second player is the opposite. In this paper, necessary and sufficient termination conditions are found, and optimal controls of the players are constructed.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72890783","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}
Pub Date : 2021-11-01DOI: 10.35634/2226-3594-2021-58-05
V. Ushakov, A. Ushakov, O. Kuvshinov
The problem of getting close of a controlled system with a compact space in a finite-dimensional Euclidean space at a fixed time is studied. A method of constructing a solution to the problem is proposed which is based on the ideology of the maximum shift of the motion of the controlled system by the solvability set of the getting close problem.
{"title":"On the construction of resolving control in the problem of getting close at a fixed time moment","authors":"V. Ushakov, A. Ushakov, O. Kuvshinov","doi":"10.35634/2226-3594-2021-58-05","DOIUrl":"https://doi.org/10.35634/2226-3594-2021-58-05","url":null,"abstract":"The problem of getting close of a controlled system with a compact space in a finite-dimensional Euclidean space at a fixed time is studied. A method of constructing a solution to the problem is proposed which is based on the ideology of the maximum shift of the motion of the controlled system by the solvability set of the getting close problem.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84413766","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}
Pub Date : 2021-11-01DOI: 10.35634/2226-3594-2021-58-04
A. Kazakov, A. Lempert
The article deals with the vehicle routing problem in an environment with dynamically changing properties. The problem is relevant in current conditions when the delivery cost has a steady upward trend and is often comparable to the cost of the product itself. A central feature of the study is that the optimality criterion is the minimum delivery time, but not the distance traveled. The optical-geometric approach developed by the authors, based on the analogy between the propagation of light in an optically inhomogeneous medium and the minimization of the integral functional, is used as a research tool. We use exact and approximate solutions of the eikonal equations to describe wave fronts. Two original numerical algorithms for route construction are proposed and implemented as software. A computational experiment is performed that justified the effectiveness of the proposed model-algorithmic tools.
{"title":"On the route construction in changing environments using solutions of the eikonal equation","authors":"A. Kazakov, A. Lempert","doi":"10.35634/2226-3594-2021-58-04","DOIUrl":"https://doi.org/10.35634/2226-3594-2021-58-04","url":null,"abstract":"The article deals with the vehicle routing problem in an environment with dynamically changing properties. The problem is relevant in current conditions when the delivery cost has a steady upward trend and is often comparable to the cost of the product itself. A central feature of the study is that the optimality criterion is the minimum delivery time, but not the distance traveled. The optical-geometric approach developed by the authors, based on the analogy between the propagation of light in an optically inhomogeneous medium and the minimization of the integral functional, is used as a research tool. We use exact and approximate solutions of the eikonal equations to describe wave fronts. Two original numerical algorithms for route construction are proposed and implemented as software. A computational experiment is performed that justified the effectiveness of the proposed model-algorithmic tools.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80807740","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}
Pub Date : 2021-11-01DOI: 10.35634/2226-3594-2021-58-01
T. M. Bannikova, V. Nemtsov, N. Baranova, G. Konygin, O. Nemtsova
A method for obtaining the interval of statistical error of the solution of the inverse spectroscopy problem, for the estimation of the statistical error of experimental data of which the normal distribution law can be applied, has been proposed. With the help of mathematical modeling of the statistical error of partial spectral components obtained from the numerically stable solution of the inverse problem, it has become possible to specify the error of the corresponding solution. The problem of getting the inverse solution error interval is actual because the existing methods of solution error evaluation are based on the analysis of smooth functional dependences under rigid restrictions on the region of acceptable solutions (compactness, monotonicity, etc.). Their use in computer processing of real experimental data is extremely difficult and therefore, as a rule, is not applied. Based on the extraction of partial spectral components and the estimation of their error, a method for obtaining an interval of statistical error for the solution of inverse spectroscopy problems has been proposed in this work. The necessity and importance of finding the solution error interval to provide reliable results is demonstrated using examples of processing Mössbauer spectra.
{"title":"A method for estimating the statistical error of the solution in the inverse spectroscopy problem","authors":"T. M. Bannikova, V. Nemtsov, N. Baranova, G. Konygin, O. Nemtsova","doi":"10.35634/2226-3594-2021-58-01","DOIUrl":"https://doi.org/10.35634/2226-3594-2021-58-01","url":null,"abstract":"A method for obtaining the interval of statistical error of the solution of the inverse spectroscopy problem, for the estimation of the statistical error of experimental data of which the normal distribution law can be applied, has been proposed. With the help of mathematical modeling of the statistical error of partial spectral components obtained from the numerically stable solution of the inverse problem, it has become possible to specify the error of the corresponding solution. The problem of getting the inverse solution error interval is actual because the existing methods of solution error evaluation are based on the analysis of smooth functional dependences under rigid restrictions on the region of acceptable solutions (compactness, monotonicity, etc.). Their use in computer processing of real experimental data is extremely difficult and therefore, as a rule, is not applied. Based on the extraction of partial spectral components and the estimation of their error, a method for obtaining an interval of statistical error for the solution of inverse spectroscopy problems has been proposed in this work. The necessity and importance of finding the solution error interval to provide reliable results is demonstrated using examples of processing Mössbauer spectra.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81208954","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}
Pub Date : 2021-11-01DOI: 10.35634/2226-3594-2021-58-02
L. I. Danilov
We prove absolute continuity of the spectrum of a periodic $n$-dimensional Schrödinger operator for $ngeqslant 4$. Certain conditions on the magnetic potential $A$ and the electric potential $V+sum f_jdelta_{S_j}$ are supposed to be fulfilled. In particular, we can assume that the following conditions are satisfied. (1) The magnetic potential $Acolon{mathbb{R}}^nto{mathbb{R}}^n$ either has an absolutely convergent Fourier series or belongs to the space $H^q_{mathrm{loc}}({mathbb{R}}^n;{mathbb{R}}^n)$, $2q>n-1$, or to the space $C({mathbb{R}}^n;{mathbb{R}}^n)cap H^q_{mathrm{loc}}({mathbb{R}}^n;{mathbb{R}}^n)$, $2q>n-2$. (2) The function $Vcolon{mathbb{R}}^ntomathbb{R}$ belongs to Morrey space ${mathfrak{L}}^{2,p}$, $pin big(frac{n-1}{2},frac{n}{2}big]$, of periodic functions (with a given period lattice), and $$limlimits_{tauto+0}suplimits_{00$ centered at a point $xin{mathbb{R}}^n$, $B^n_r=B^n_r(0)$, $v(B^n_r)$ is volume of the ball $B^n_r$, $C=C(n,p;A)>0$. (3) $delta_{S_j}$ are $delta$-functions concentrated on (piecewise) $C^1$-smooth periodic hypersurfaces $S_j$, $f_jin L^p_{mathrm{loc}}(S_j)$, $j=1,ldots,m$. Some additional geometric conditions are imposed on the hypersurfaces $S_j$, and these conditions determine the choice of numbers $pgeqslant n-1$. In particular, let hypersurfaces $S_j$ be $C^2$-smooth, the unit vector $e$ be arbitrarily taken from some dense set of the unit sphere $S^{n-1}$ dependent on the magnetic potential $A$, and the normal curvature of the hypersurfaces $S_j$ in the direction of the unit vector $e$ be nonzero at all points of tangency of the hypersurfaces $S_j$ and the lines ${x_0+tecolon tinmathbb{R}}$, $x_0in{mathbb{R}}^n$. Then we can choose the number $p>frac{3n}{2}-3$, $ngeqslant 4$.
{"title":"On the spectrum of a multidimensional periodic magnetic Shrödinger operator with a singular electric potential","authors":"L. I. Danilov","doi":"10.35634/2226-3594-2021-58-02","DOIUrl":"https://doi.org/10.35634/2226-3594-2021-58-02","url":null,"abstract":"We prove absolute continuity of the spectrum of a periodic $n$-dimensional Schrödinger operator for $ngeqslant 4$. Certain conditions on the magnetic potential $A$ and the electric potential $V+sum f_jdelta_{S_j}$ are supposed to be fulfilled. In particular, we can assume that the following conditions are satisfied.\u0000(1) The magnetic potential $Acolon{mathbb{R}}^nto{mathbb{R}}^n$ either has an absolutely convergent Fourier series or belongs to the space $H^q_{mathrm{loc}}({mathbb{R}}^n;{mathbb{R}}^n)$, $2q>n-1$, or to the space $C({mathbb{R}}^n;{mathbb{R}}^n)cap H^q_{mathrm{loc}}({mathbb{R}}^n;{mathbb{R}}^n)$, $2q>n-2$.\u0000(2) The function $Vcolon{mathbb{R}}^ntomathbb{R}$ belongs to Morrey space ${mathfrak{L}}^{2,p}$, $pin big(frac{n-1}{2},frac{n}{2}big]$, of periodic functions (with a given period lattice), and\u0000$$limlimits_{tauto+0}suplimits_{00$ centered at a point $xin{mathbb{R}}^n$, $B^n_r=B^n_r(0)$, $v(B^n_r)$ is volume of the ball $B^n_r$, $C=C(n,p;A)>0$.\u0000(3) $delta_{S_j}$ are $delta$-functions concentrated on (piecewise) $C^1$-smooth periodic hypersurfaces $S_j$, $f_jin L^p_{mathrm{loc}}(S_j)$, $j=1,ldots,m$. Some additional geometric conditions are imposed on the hypersurfaces $S_j$, and these conditions determine the choice of numbers $pgeqslant n-1$. In particular, let hypersurfaces $S_j$ be $C^2$-smooth, the unit vector $e$ be arbitrarily taken from some dense set of the unit sphere $S^{n-1}$ dependent on the magnetic potential $A$, and the normal curvature of the hypersurfaces $S_j$ in the direction of the unit vector $e$ be nonzero at all points of tangency of the hypersurfaces $S_j$ and the lines ${x_0+tecolon tinmathbb{R}}$, $x_0in{mathbb{R}}^n$. Then we can choose the number $p>frac{3n}{2}-3$, $ngeqslant 4$.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82204150","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}
Pub Date : 2021-05-01DOI: 10.35634/2226-3594-2021-57-07
V. Pimenov, E. Tashirova
For a fractional diffusion-wave equation with a nonlinear effect of functional delay, an implicit numerical method is constructed. The scheme is based on the L2-method of approximation of the fractional derivative of the order from 1 to 2, interpolation and extrapolation with the given properties of discrete prehistory and an analogue of the Crank-Nicolson method. The order of convergence of the method is investigated using the ideas of the general theory of difference schemes with heredity. The order of convergence of the method is more significant than in previously known methods, depending on the order of the starting values. The main point of the proof is the use of the stability of the L2-method. The results of comparing numerical experiments with other schemes are presented: a purely implicit method and a purely explicit method, these results showed, in general, the advantages of the proposed scheme.
{"title":"Numerical method for fractional diffusion-wave equations with functional delay","authors":"V. Pimenov, E. Tashirova","doi":"10.35634/2226-3594-2021-57-07","DOIUrl":"https://doi.org/10.35634/2226-3594-2021-57-07","url":null,"abstract":"For a fractional diffusion-wave equation with a nonlinear effect of functional delay, an implicit numerical method is constructed. The scheme is based on the L2-method of approximation of the fractional derivative of the order from 1 to 2, interpolation and extrapolation with the given properties of discrete prehistory and an analogue of the Crank-Nicolson method. The order of convergence of the method is investigated using the ideas of the general theory of difference schemes with heredity. The order of convergence of the method is more significant than in previously known methods, depending on the order of the starting values. The main point of the proof is the use of the stability of the L2-method. The results of comparing numerical experiments with other schemes are presented: a purely implicit method and a purely explicit method, these results showed, in general, the advantages of the proposed scheme.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86295720","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}
Pub Date : 2020-11-01DOI: 10.35634/2226-3594-2020-56-01
V. Zaitsev, I. G. Kim
A linear control system defined by a stationary differential equation of nth order with several commensurate lumped and distributed delays in state is considered. In the system, the input is a linear combination of m variables and their derivatives of order not more than n−p and the output is a k-dimensional vector of linear combinations of the state and its derivatives of order not more than p−1. For this system, a spectrum assignment problem by linear static output feedback with commensurate lumped and distributed delays is studied. Necessary and sufficient conditions are obtained for solvability of the arbitrary spectrum assignment problem by static output feedback controller. Corollaries on stabilization of the system are obtained.
{"title":"Spectrum assignment in linear systems with several commensurate lumped and distributed delays in state by means of static output feedback","authors":"V. Zaitsev, I. G. Kim","doi":"10.35634/2226-3594-2020-56-01","DOIUrl":"https://doi.org/10.35634/2226-3594-2020-56-01","url":null,"abstract":"A linear control system defined by a stationary differential equation of nth order with several commensurate lumped and distributed delays in state is considered. In the system, the input is a linear combination of m variables and their derivatives of order not more than n−p and the output is a k-dimensional vector of linear combinations of the state and its derivatives of order not more than p−1. For this system, a spectrum assignment problem by linear static output feedback with commensurate lumped and distributed delays is studied. Necessary and sufficient conditions are obtained for solvability of the arbitrary spectrum assignment problem by static output feedback controller. Corollaries on stabilization of the system are obtained.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89418172","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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