Výsledky vyhledávání - "S. Ya. Serovaiskii"

An optimal control problem for a nonlinear elliptic equation with a phase constraint and state variation

Autor: S. Ya. Serovaiskii

Publikováno v: Russian Mathematics. 57:67-70

We study an optimal control problem for a system described by a nonlinear elliptic equation with a state constraint in the form of an inclusion. We prove the solvability of the problem under consideration and by varying the state of the system obtain

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::da752f72929af77ba644781030c75dbe
https://doi.org/10.3103/s1066369x13090119

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Approximation methods in optimal control problems for nonlinear infinite-dimensional systems

Autor: S. Ya. Serovaiskii

Publikováno v: Mathematical Notes. 94:567-582

Some notions related to approximate solutions and to the approximation of extremum problems for nonlinear infinite-dimensional systems are proposed. Optimization problems for nonlinear parabolic equations with a fixed terminal state and on an infinit

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::96a4e30e36d9a13516d9fa315e882358
https://doi.org/10.1134/s0001434613090277

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Optimal control of nonlinear evolution systems in the case where the solution is not differentiable with respect to the control

Autor: S. Ya. Serovaiskii

Publikováno v: Mathematical Notes. 93:593-606

For the simplest heat equation with power nonlinearity, the dependence of the solution of the corresponding boundary-value problem on the constant term of the equation turns out to be, in general, not differentiable in the sense of Gâteaux.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::9865d88b914ee602dadc353a6a459917
https://doi.org/10.1134/s0001434613030280

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Elements of the theory and methods of parametric regulation of national economy’s evolution using discrete dynamic stochastic models

Autor: Bahyt T. Sultanov, S. Ya. Serovaiskii, Askar A. Ashimov, Dmitry A. Novikov, Yu. V. Borovskii, As. A. Ashimov

Publikováno v: Automation and Remote Control. 73:1156-1164

For the class of discreet stochastic dynamic systems with additive noise, advances of the theory of parametric regulation were presented. Efficiency of their use was demonstrated by way of the example of a stochastic computable model of general equil

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::79992950fc83f990fad3ebd29b437ab1
https://doi.org/10.1134/s0005117912070053

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The necessary optimality conditions for a nonlinear stationary system whose state functional is not differentiable with respect to the control

Autor: S. Ya. Serovaiskii

Publikováno v: Russian Mathematics. 54:26-38

We consider a control system described by a nonlinear elliptic equation. Its control-state mapping is extendedly differentiable but not Gateaux differentiable for large values of the domain dimension and the nonlinearity index. We obtain the necessar

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::25799dfbd074db43927d38fef9d7b25d
https://doi.org/10.3103/s1066369x10060046

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Differentiation of operators and optimality conditions in category interpretation

Autor: S. Ya. Serovaiskii

Publikováno v: Russian Mathematics. 54:57-65

The general extremum theory essentially uses properties of operator derivatives. As an example we consider a system described by a nonlinear elliptic equation. In this system with large values of the nonlinearity parameter and the domain dimension th

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::5782a725872b30a43b1829e44adece54
https://doi.org/10.3103/s1066369x10020076

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Optimization for nonlinear hyperbolic equations without the uniqueness theorem for a solution of the boundary-value problem

Autor: S. Ya. Serovaiskii

Publikováno v: Russian Mathematics. 53:64-70

We consider the optimal control problem for a system governed by a nonlinear hyperbolic equation without any constraints on the parameter of nonlinearity. No uniqueness theorem is established for a solution to this problem. The control-state mapping

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::061911162ecd0894772bfc38c4520528
https://doi.org/10.3103/s1066369x09010046

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The sequential differentiation and its applications in the optimal control problems

Autor: S. Ya. Serovaiskii

Publikováno v: Russian Mathematics. 52:38-47

Using the sequential approach, we define a certain generalization of the operator derivative. We establish the necessary extremum condition in terms of the sequential derivative. As examples we consider the optimal control problems for systems govern

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b8fde8661c1166567222abae9841df91
https://doi.org/10.3103/s1066369x08070062

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