Theoretical Aspects of Constructing a Neurocontroller for Switched Systems
We consider the problem of stabilizing a switched linear system with slow switchings that cannot be observed. The solution is sought in the class of variable structure controllers. To ensure the operability of such a controller, it is necessary to construct a switching signal observer. As an observe...
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| Published in | Differential equations Vol. 58; no. 11; pp. 1549 - 1557 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
01.11.2022
Springer Springer Nature B.V |
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| Abstract | We consider the problem of stabilizing a switched linear system with slow switchings that cannot be observed. The solution is sought in the class of variable structure controllers. To ensure the operability of such a controller, it is necessary to construct a switching signal observer. As an observer, it is proposed to use a neural network. The theoretical aspects of adjusting such an observer are the subject of this paper. |
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| AbstractList | We consider the problem of stabilizing a switched linear system with slow switchings that cannot be observed. The solution is sought in the class of variable structure controllers. To ensure the operability of such a controller, it is necessary to construct a switching signal observer. As an observer, it is proposed to use a neural network. The theoretical aspects of adjusting such an observer are the subject of this paper. We consider the problem of stabilizing a switched linear system with slow switchings thatcannot be observed. The solution is sought in the class of variable structure controllers. To ensurethe operability of such a controller, it is necessary to construct a switching signal observer. As anobserver, it is proposed to use a neural network. The theoretical aspects of adjusting such anobserver are the subject of this paper. |
| Audience | Academic |
| Author | Fursov, A. S. Mosolova, Yu. M. |
| Author_xml | – sequence: 1 givenname: A. S. surname: Fursov fullname: Fursov, A. S. email: fursov@cs.msu.ru organization: Department of Mathematics, School of Science, Hangzhou Dianzi University, Lomonosov Moscow State University, Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences – sequence: 2 givenname: Yu. M. surname: Mosolova fullname: Mosolova, Yu. M. email: july2412@mail.ru organization: Lomonosov Moscow State University |
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| References | AndreevYu.N.Upravlenie konechnomernymi lineinymi ob”ektami (Control of Finite-Dimensional Linear Plants)1976MoscowNauka0353.93003 DemidovichB.P.Lektsii po matematicheskoi teorii ustoichivosti (Lectures on the Mathematical Theory of Stability)1967MoscowNauka BalandinD.V.KoganM.M.Sintez zakonov upravleniya na osnove lineinykh matrichnykh neravenstv (Synthesis of Control Laws Based on Linear Matrix Inequalities)2007MoscowFizmatlit FursovA.S.KhusainovE.F.On the stabilization of switchable linear systemsDiffer. Equations2015511115181528345316810.1134/S00122661151101301332.93318 LiberzonD.Switching in Systems and Control2003BostonSpringer10.1007/978-1-4612-0017-81036.93001 FursovA.S.KhusainovE.F.Superstabilization of linear dynamic plants under operator disturbancesDiffer. Equations2014507854865332684110.1134/S00122661140700271302.93175 HaykinS.Neural Networks1999Upper Saddle River, NJPrentice-Hall0934.68076 PolyakB.T.ShcherbakovP.S.Superstable linear control systems. I. AnalysisAutom. Remote Control20026383753192714510.1023/A:10198232085921094.93510 FursovA.S.MosolovaY.M.MinyaevS.I.Digital superstabilization of a switched interval linear systemDiffer. Equations2020561114851495419399310.1134/S001226612001100991454.93158 D.V. Balandin (2445_CR1) 2007 A.S. Fursov (2445_CR6) 2015; 51 Yu.N. Andreev (2445_CR4) 1976 D. Liberzon (2445_CR5) 2003 B.T. Polyak (2445_CR2) 2002; 63 A.S. Fursov (2445_CR3) 2020; 56 B.P. Demidovich (2445_CR9) 1967 A.S. Fursov (2445_CR7) 2014; 50 S. Haykin (2445_CR8) 1999 |
| References_xml | – reference: FursovA.S.KhusainovE.F.On the stabilization of switchable linear systemsDiffer. Equations2015511115181528345316810.1134/S00122661151101301332.93318 – reference: FursovA.S.KhusainovE.F.Superstabilization of linear dynamic plants under operator disturbancesDiffer. Equations2014507854865332684110.1134/S00122661140700271302.93175 – reference: DemidovichB.P.Lektsii po matematicheskoi teorii ustoichivosti (Lectures on the Mathematical Theory of Stability)1967MoscowNauka – reference: BalandinD.V.KoganM.M.Sintez zakonov upravleniya na osnove lineinykh matrichnykh neravenstv (Synthesis of Control Laws Based on Linear Matrix Inequalities)2007MoscowFizmatlit – reference: FursovA.S.MosolovaY.M.MinyaevS.I.Digital superstabilization of a switched interval linear systemDiffer. Equations2020561114851495419399310.1134/S001226612001100991454.93158 – reference: AndreevYu.N.Upravlenie konechnomernymi lineinymi ob”ektami (Control of Finite-Dimensional Linear Plants)1976MoscowNauka0353.93003 – reference: LiberzonD.Switching in Systems and Control2003BostonSpringer10.1007/978-1-4612-0017-81036.93001 – reference: PolyakB.T.ShcherbakovP.S.Superstable linear control systems. I. AnalysisAutom. Remote Control20026383753192714510.1023/A:10198232085921094.93510 – reference: HaykinS.Neural Networks1999Upper Saddle River, NJPrentice-Hall0934.68076 – volume-title: Sintez zakonov upravleniya na osnove lineinykh matrichnykh neravenstv (Synthesis of Control Laws Based on Linear Matrix Inequalities) year: 2007 ident: 2445_CR1 – volume: 51 start-page: 1518 issue: 11 year: 2015 ident: 2445_CR6 publication-title: Differ. Equations doi: 10.1134/S0012266115110130 – volume: 56 start-page: 1485 issue: 11 year: 2020 ident: 2445_CR3 publication-title: Differ. Equations doi: 10.1134/S00122661200110099 – volume-title: Lektsii po matematicheskoi teorii ustoichivosti (Lectures on the Mathematical Theory of Stability) year: 1967 ident: 2445_CR9 – volume-title: Upravlenie konechnomernymi lineinymi ob”ektami (Control of Finite-Dimensional Linear Plants) year: 1976 ident: 2445_CR4 – volume: 50 start-page: 854 issue: 7 year: 2014 ident: 2445_CR7 publication-title: Differ. Equations doi: 10.1134/S0012266114070027 – volume-title: Neural Networks year: 1999 ident: 2445_CR8 – volume-title: Switching in Systems and Control year: 2003 ident: 2445_CR5 doi: 10.1007/978-1-4612-0017-8 – volume: 63 start-page: 37 issue: 8 year: 2002 ident: 2445_CR2 publication-title: Autom. Remote Control doi: 10.1023/A:1019823208592 |
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| Snippet | We consider the problem of stabilizing a switched linear system with slow switchings that cannot be observed. The solution is sought in the class of variable... We consider the problem of stabilizing a switched linear system with slow switchings thatcannot be observed. The solution is sought in the class of variable... |
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| SubjectTerms | Control Theory Difference and Functional Equations Differential equations Mathematics Mathematics and Statistics Neural networks Ordinary Differential Equations Partial Differential Equations Variable structure control |
| Title | Theoretical Aspects of Constructing a Neurocontroller for Switched Systems |
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