On the unimprovability of full-memory strategies in the risk minimization problem
Methods from the theory of guaranteeing positional control are used to study the risk minimization problem, i.e., the problem of optimal control under dynamic disturbances in a formalization based on the Savage criterion. A control system described by an ordinary differential equation is considered....
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| Published in | Proceedings of the Steklov Institute of Mathematics Vol. 287; no. Suppl 1; pp. 175 - 184 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
01.12.2014
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0081-5438 1531-8605 |
| DOI | 10.1134/S008154381409017X |
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| Abstract | Methods from the theory of guaranteeing positional control are used to study the risk minimization problem, i.e., the problem of optimal control under dynamic disturbances in a formalization based on the Savage criterion. A control system described by an ordinary differential equation is considered. The values of control actions and disturbance at each moment lie in known compact sets. Realizations of the disturbance are also subject to an unknown functional constraint from a given set of functional constraints. Realizations of the control are formed by full-memory positional strategies. The quality functional, which is defined on motions of the control system, is assumed to be continuous on the corresponding space of continuous functions. New conditions that provide the unimprovability of the class of fullmemory positional strategies under program constraints and
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-compact constraints on the disturbance are presented. |
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| AbstractList | Methods from the theory of guaranteeing positional control are used to study the risk minimization problem, i.e., the problem of optimal control under dynamic disturbances in a formalization based on the Savage criterion. A control system described by an ordinary differential equation is considered. The values of control actions and disturbance at each moment lie in known compact sets. Realizations of the disturbance are also subject to an unknown functional constraint from a given set of functional constraints. Realizations of the control are formed by full-memory positional strategies. The quality functional, which is defined on motions of the control system, is assumed to be continuous on the corresponding space of continuous functions. New conditions that provide the unimprovability of the class of fullmemory positional strategies under program constraints and
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2
-compact constraints on the disturbance are presented. |
| Author | Serkov, D. A. |
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| Keywords | functionally limited disturbance Savage criterion full-memory strategy |
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| References | SubbotinA IChentsovA GGuarantee Optimization in Control Problems1981MoscowNauka0542.90106 KrasovskiiN NControl of a Dynamical System1985MoscowNauka BarabanovaN NSubbotinA IOn classes of strategies in differential games of evasion of contactJ. Appl. Math. Mech.197135334935610.1016/0021-8928(71)90001-30247.90082354048 KrasovskiiN NGame Problems on the Encounter of Motions1970MoscowNauka0246.90060 KryazhimskiiA VOsipovYu SModelling of a control in a dynamic systemEngrg. Cybernetics19842123847746678 SerkovD AOptimization of guaranteed results under functional restrictions on the dynamic disturbanceDokl. Math.201387331031310.1134/S10645624130301131277.490293114490 OsipovYu SKryazhimskiiA VInverse Problems for Ordinary Differential Equations: Dynamical Solutions1995LondonGordon and Breach0884.34015 KrasovskiiN NSubbotinA IPositional Differential Games1974MoscowNauka0298.90067 BarabanovaN NSubbotinA IOn continuous evasion strategies in game problems on the encounter of motionsJ. Appl. Math. Mech.197034576577210.1016/0021-8928(70)90057-20256.90060312918 WargaJOptimal Control of Differential and Functional Equations1972New YorkAcademic0253.49001 SavageL JThe theory of statistical decisionJ. Amer. Stat. Assoc.195146556710.1080/01621459.1951.105007680042.14302 SerkovD ARisk-optimal control under functional constraints on the disturbanceMat. Teor. Igr Prilozh.201351741031273.91102 KryazhimskiiA VRassiasT MThe problem of optimization of the ensured result: Unimprovability of full-memory strategiesConstantin Carathéodory: An International Tribute1991Teaneck, NJWorld Sci.63667510.1142/9789814350921_0037 NiehansJZur Preisbildung bei ungewissen ErwartungenSchweiz. Z. Volkswirtsch. Stat.1948845433456 A V Kryazhimskii (6826_CR10) 1984; 21 A V Kryazhimskii (6826_CR7) 1991 J Niehans (6826_CR8) 1948; 84 D A Serkov (6826_CR12) 2013; 5 N N Barabanova (6826_CR5) 1970; 34 D A Serkov (6826_CR13) 2013; 87 N N Krasovskii (6826_CR4) 1970 Yu S Osipov (6826_CR11) 1995 N N Krasovskii (6826_CR2) 1985 J Warga (6826_CR14) 1972 A I Subbotin (6826_CR3) 1981 N N Krasovskii (6826_CR1) 1974 L J Savage (6826_CR9) 1951; 46 N N Barabanova (6826_CR6) 1971; 35 |
| References_xml | – reference: SerkovD ARisk-optimal control under functional constraints on the disturbanceMat. Teor. Igr Prilozh.201351741031273.91102 – reference: NiehansJZur Preisbildung bei ungewissen ErwartungenSchweiz. Z. Volkswirtsch. Stat.1948845433456 – reference: OsipovYu SKryazhimskiiA VInverse Problems for Ordinary Differential Equations: Dynamical Solutions1995LondonGordon and Breach0884.34015 – reference: SavageL JThe theory of statistical decisionJ. Amer. Stat. Assoc.195146556710.1080/01621459.1951.105007680042.14302 – reference: BarabanovaN NSubbotinA IOn classes of strategies in differential games of evasion of contactJ. Appl. Math. Mech.197135334935610.1016/0021-8928(71)90001-30247.90082354048 – reference: KrasovskiiN NSubbotinA IPositional Differential Games1974MoscowNauka0298.90067 – reference: SubbotinA IChentsovA GGuarantee Optimization in Control Problems1981MoscowNauka0542.90106 – reference: SerkovD AOptimization of guaranteed results under functional restrictions on the dynamic disturbanceDokl. Math.201387331031310.1134/S10645624130301131277.490293114490 – reference: KrasovskiiN NGame Problems on the Encounter of Motions1970MoscowNauka0246.90060 – reference: KryazhimskiiA VOsipovYu SModelling of a control in a dynamic systemEngrg. Cybernetics19842123847746678 – reference: KryazhimskiiA VRassiasT MThe problem of optimization of the ensured result: Unimprovability of full-memory strategiesConstantin Carathéodory: An International Tribute1991Teaneck, NJWorld Sci.63667510.1142/9789814350921_0037 – reference: BarabanovaN NSubbotinA IOn continuous evasion strategies in game problems on the encounter of motionsJ. Appl. Math. Mech.197034576577210.1016/0021-8928(70)90057-20256.90060312918 – reference: KrasovskiiN NControl of a Dynamical System1985MoscowNauka – reference: WargaJOptimal Control of Differential and Functional Equations1972New YorkAcademic0253.49001 – volume: 84 start-page: 433 issue: 5 year: 1948 ident: 6826_CR8 publication-title: Schweiz. Z. Volkswirtsch. Stat. – volume: 34 start-page: 765 issue: 5 year: 1970 ident: 6826_CR5 publication-title: J. Appl. Math. Mech. doi: 10.1016/0021-8928(70)90057-2 – volume: 87 start-page: 310 issue: 3 year: 2013 ident: 6826_CR13 publication-title: Dokl. Math. doi: 10.1134/S1064562413030113 – volume-title: Positional Differential Games year: 1974 ident: 6826_CR1 – start-page: 636 volume-title: Constantin Carathéodory: An International Tribute year: 1991 ident: 6826_CR7 doi: 10.1142/9789814350921_0037 – volume: 5 start-page: 74 issue: 1 year: 2013 ident: 6826_CR12 publication-title: Mat. Teor. Igr Prilozh. – volume-title: Game Problems on the Encounter of Motions year: 1970 ident: 6826_CR4 – volume: 21 start-page: 38 issue: 2 year: 1984 ident: 6826_CR10 publication-title: Engrg. Cybernetics – volume-title: Guarantee Optimization in Control Problems year: 1981 ident: 6826_CR3 – volume: 35 start-page: 349 issue: 3 year: 1971 ident: 6826_CR6 publication-title: J. Appl. Math. Mech. doi: 10.1016/0021-8928(71)90001-3 – volume: 46 start-page: 55 year: 1951 ident: 6826_CR9 publication-title: J. Amer. Stat. Assoc. doi: 10.1080/01621459.1951.10500768 – volume-title: Inverse Problems for Ordinary Differential Equations: Dynamical Solutions year: 1995 ident: 6826_CR11 – volume-title: Optimal Control of Differential and Functional Equations year: 1972 ident: 6826_CR14 – volume-title: Control of a Dynamical System year: 1985 ident: 6826_CR2 |
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| Title | On the unimprovability of full-memory strategies in the risk minimization problem |
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