The successive parameterization method of control actions in boundary value optimal control problems for distributed parameter systems
A special procedure for control action parameterization and the precise method based on it for determining open-loop optimal control algorithms for the systems with distributed parameters under the prescribed tolerance conditions for the deviation from the required final state of the controlled para...
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| Vydáno v: | Journal of computer & systems sciences international Ročník 48; číslo 3; s. 351 - 362 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Dordrecht
SP MAIK Nauka/Interperiodica
01.06.2009
Springer Nature B.V |
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| ISSN: | 1064-2307, 1555-6530 |
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| Abstract | A special procedure for control action parameterization and the precise method based on it for determining open-loop optimal control algorithms for the systems with distributed parameters under the prescribed tolerance conditions for the deviation from the required final state of the controlled parameter being estimated in the uniform metric is proposed. The method uses the reduction to the problems of semi-infinite optimization, alternance properties of their solutions, and some additional information on fundamental regularities of the subject domain. Examples showing an opportunity of using these results for applied problems, constituting also a point of independent interest are presented. |
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| AbstractList | A special procedure for control action parameterization and the precise method based on it for determining open-loop optimal control algorithms for the systems with distributed parameters under the prescribed tolerance conditions for the deviation from the required final state of the controlled parameter being estimated in the uniform metric is proposed. The method uses the reduction to the problems of semi-infinite optimization, alternance properties of their solutions, and some additional information on fundamental regularities of the subject domain. Examples showing an opportunity of using these results for applied problems, constituting also a point of independent interest are presented. A special procedure for control action parameterization and the precise method based on it for determining open-loop optimal control algorithms for the systems with distributed parameters under the prescribed tolerance conditions for the deviation from the required final state of the controlled parameter being estimated in the uniform metric is proposed. The method uses the reduction to the problems of semi-infinite optimization, alternance properties of their solutions, and some additional information on fundamental regularities of the subject domain. Examples showing an opportunity of using these results for applied problems, constituting also a point of independent interest are presented.[PUBLICATION ABSTRACT] |
| Author | Pleshivtseva, Yu. E. Rapoport, E. Ya |
| Author_xml | – sequence: 1 givenname: Yu. E. surname: Pleshivtseva fullname: Pleshivtseva, Yu. E. organization: Samara State Technical University – sequence: 2 givenname: E. Ya surname: Rapoport fullname: Rapoport, E. Ya organization: Samara State Technical University |
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| DOI | 10.1134/S1064230709030034 |
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| References | RapoportE. Ya.Structural Simulation of Objects and Systems with Distributed Parameters2003MoscowVysshaya Shkola KollattsL.KrabsV.Approximation Theory. Chebyshev Approximations1978MoscowNauka ButkovskiiA. G.MalyiS. A.AndreevYu. N.Optimal Control for Heating Metals1981MoscowMetallurgiya GabasovR.KirillovaF. M.Singular Optimal Controls1973MoscowNauka MoiseevN. N.Elements of the Theory of Optimal Systems1975MoscowNauka RapoportE. Ya.Altrnance Method in Applied Optimization Problems2000MoscowNauka FedorenkoR. P.Approximate Solution of Optimal Control Problems1978MoscowNauka0462.49001 ButkovskiiA. G.The Theory of Optimal Control of Systems with Distributed Parameters1965MoscowNauka ButkovskiiA. G.Control Methods for Systems with Distributed Parameters1975MoscowNauka E. Ya. Rapoport, “Alternance Properties of Optimal Solutions and Computational Algorithms in Problems of Semi-infinite Optimization of Controlled Systems,” Izv. Ross. Akad. Nauk, Teor. Sist. Upr., No. 4, 84–95 (1996) [Comp. Syst. Sci. 35 (4), 581–591 (1996)]. KarlinS.StaddenV.Chebyshev Systems and Their Application in Analysis and Statistics1976MoscowNauka Vasil’evF. P.Optimization Methods2002MoscowFaktorial Press PleshivtsevaYu. E.Algorithms of Suboptimal Spatial—Temporal Control for a System with Distributed ParametersElements and Systems of Optimal Identification and Control of Technological Processes1994TulaTulGTU8091 RapoportE. Ya.Optimization of Processes of Induction Heating of Metals1993MoscowMetallurgiya RapoportE. Ya.Analysis and Synthesis of Control Systems with Distributed Parameters2005MoscowVysshaya Shkola E. Ya. Rapoport, “To Development of Applied Control Theory,” Mekhatronika, Avtomatizatsiya, Upravlenie, No. 6, 2–14 (2004). RapoportE. Ya.PleshivtsevaYu. E.Optimal Control of Induction Heating Processes2007Voca Raton, London, New YorkCRC Press, Taylor & Francis Group Yu. V. Egorov, “A Necessary Optimality Condition in the Banach Space,” Mat. sb. (new series) 64(106) (1), (1964). RapoportE. Ya.MatrosovV. M.Vasil’evaS. N.MoskalenkoA. I.Altrnance Method in Problems of Semi-Infinite OptimizationNonlinear Control Theory and Its Applications: Dynamics, Control, Optimization2003MoscowFizmatlit ButkovskiiA. G.Structural Theory of Distributed Systems1977MoscowNauka 3003_CR8 Yu. E. Pleshivtseva (3003_CR14) 1994 A. G. Butkovskii (3003_CR4) 1965 R. Gabasov (3003_CR20) 1973 A. G. Butkovskii (3003_CR5) 1975 A. G. Butkovskii (3003_CR12) 1977 E. Ya. Rapoport (3003_CR13) 2007 E. Ya. Rapoport (3003_CR7) 2005 N. N. Moiseev (3003_CR1) 1975 3003_CR11 A. G. Butkovskii (3003_CR19) 1981 E. Ya. Rapoport (3003_CR10) 2003 E. Ya. Rapoport (3003_CR15) 2003 E. Ya. Rapoport (3003_CR6) 1993 R. P. Fedorenko (3003_CR2) 1978 E. Ya. Rapoport (3003_CR9) 2000 3003_CR16 F. P. Vasil’ev (3003_CR3) 2002 L. Kollatts (3003_CR18) 1978 S. Karlin (3003_CR17) 1976 |
| References_xml | – reference: E. Ya. Rapoport, “Alternance Properties of Optimal Solutions and Computational Algorithms in Problems of Semi-infinite Optimization of Controlled Systems,” Izv. Ross. Akad. Nauk, Teor. Sist. Upr., No. 4, 84–95 (1996) [Comp. Syst. Sci. 35 (4), 581–591 (1996)]. – reference: RapoportE. Ya.PleshivtsevaYu. E.Optimal Control of Induction Heating Processes2007Voca Raton, London, New YorkCRC Press, Taylor & Francis Group – reference: ButkovskiiA. G.Structural Theory of Distributed Systems1977MoscowNauka – reference: RapoportE. Ya.MatrosovV. M.Vasil’evaS. N.MoskalenkoA. I.Altrnance Method in Problems of Semi-Infinite OptimizationNonlinear Control Theory and Its Applications: Dynamics, Control, Optimization2003MoscowFizmatlit – reference: E. Ya. Rapoport, “To Development of Applied Control Theory,” Mekhatronika, Avtomatizatsiya, Upravlenie, No. 6, 2–14 (2004). – reference: ButkovskiiA. G.MalyiS. A.AndreevYu. N.Optimal Control for Heating Metals1981MoscowMetallurgiya – reference: KollattsL.KrabsV.Approximation Theory. Chebyshev Approximations1978MoscowNauka – reference: Vasil’evF. P.Optimization Methods2002MoscowFaktorial Press – reference: PleshivtsevaYu. E.Algorithms of Suboptimal Spatial—Temporal Control for a System with Distributed ParametersElements and Systems of Optimal Identification and Control of Technological Processes1994TulaTulGTU8091 – reference: ButkovskiiA. G.The Theory of Optimal Control of Systems with Distributed Parameters1965MoscowNauka – reference: RapoportE. Ya.Structural Simulation of Objects and Systems with Distributed Parameters2003MoscowVysshaya Shkola – reference: ButkovskiiA. G.Control Methods for Systems with Distributed Parameters1975MoscowNauka – reference: RapoportE. Ya.Optimization of Processes of Induction Heating of Metals1993MoscowMetallurgiya – reference: RapoportE. Ya.Analysis and Synthesis of Control Systems with Distributed Parameters2005MoscowVysshaya Shkola – reference: GabasovR.KirillovaF. M.Singular Optimal Controls1973MoscowNauka – reference: MoiseevN. N.Elements of the Theory of Optimal Systems1975MoscowNauka – reference: FedorenkoR. P.Approximate Solution of Optimal Control Problems1978MoscowNauka0462.49001 – reference: KarlinS.StaddenV.Chebyshev Systems and Their Application in Analysis and Statistics1976MoscowNauka – reference: Yu. V. Egorov, “A Necessary Optimality Condition in the Banach Space,” Mat. sb. (new series) 64(106) (1), (1964). – reference: RapoportE. Ya.Altrnance Method in Applied Optimization Problems2000MoscowNauka – volume-title: Approximate Solution of Optimal Control Problems year: 1978 ident: 3003_CR2 – volume-title: Optimal Control of Induction Heating Processes year: 2007 ident: 3003_CR13 – volume-title: Optimization Methods year: 2002 ident: 3003_CR3 – start-page: 80 volume-title: Elements and Systems of Optimal Identification and Control of Technological Processes year: 1994 ident: 3003_CR14 – volume-title: Structural Simulation of Objects and Systems with Distributed Parameters year: 2003 ident: 3003_CR15 – volume-title: Approximation Theory. Chebyshev Approximations year: 1978 ident: 3003_CR18 – volume-title: The Theory of Optimal Control of Systems with Distributed Parameters year: 1965 ident: 3003_CR4 – volume-title: Optimal Control for Heating Metals year: 1981 ident: 3003_CR19 – volume-title: Elements of the Theory of Optimal Systems year: 1975 ident: 3003_CR1 – volume-title: Structural Theory of Distributed Systems year: 1977 ident: 3003_CR12 – volume-title: Altrnance Method in Applied Optimization Problems year: 2000 ident: 3003_CR9 – volume-title: Optimization of Processes of Induction Heating of Metals year: 1993 ident: 3003_CR6 – ident: 3003_CR8 – volume-title: Control Methods for Systems with Distributed Parameters year: 1975 ident: 3003_CR5 – volume-title: Analysis and Synthesis of Control Systems with Distributed Parameters year: 2005 ident: 3003_CR7 – ident: 3003_CR16 – volume-title: Nonlinear Control Theory and Its Applications: Dynamics, Control, Optimization year: 2003 ident: 3003_CR10 – volume-title: Singular Optimal Controls year: 1973 ident: 3003_CR20 – ident: 3003_CR11 – volume-title: Chebyshev Systems and Their Application in Analysis and Statistics year: 1976 ident: 3003_CR17 |
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| SubjectTerms | Control Control algorithms Control in Systems with Distributed Parameters Engineering Mechatronics Robotics Studies |
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| Title | The successive parameterization method of control actions in boundary value optimal control problems for distributed parameter systems |
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