On the unimprovability of full-memory strategies in problems of guaranteed result optimization
A problem of guaranteed result optimization is considered for a control system described by an ordinary differential equation and for a performance functional that depends continuously on the trajectory of the system. The values of the control and of the disturbance satisfy compact geometric constra...
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| Published in | Proceedings of the Steklov Institute of Mathematics Vol. 291; no. Suppl 1; pp. 157 - 172 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
01.12.2015
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0081-5438 1531-8605 |
| DOI | 10.1134/S0081543815090114 |
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| Abstract | A problem of guaranteed result optimization is considered for a control system described by an ordinary differential equation and for a performance functional that depends continuously on the trajectory of the system. The values of the control and of the disturbance satisfy compact geometric constraints. It is also assumed that the realization of the disturbance is subject to an unknown functional constraint from a given set of constraints that are compact in a Lebesgue space. It is shown that the optimal guaranteed result in the class of full-memory strategies in this problem coincides with the value of the optimal guaranteed result in the class of quasi-strategies. |
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| AbstractList | A problem of guaranteed result optimization is considered for a control system described by an ordinary differential equation and for a performance functional that depends continuously on the trajectory of the system. The values of the control and of the disturbance satisfy compact geometric constraints. It is also assumed that the realization of the disturbance is subject to an unknown functional constraint from a given set of constraints that are compact in a Lebesgue space. It is shown that the optimal guaranteed result in the class of full-memory strategies in this problem coincides with the value of the optimal guaranteed result in the class of quasi-strategies. |
| Author | Serkov, D. A. |
| Author_xml | – sequence: 1 givenname: D. A. surname: Serkov fullname: Serkov, D. A. email: serkov@imm.uran.ru organization: Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Institute of Radioelectronics and Informational Technologies, Ural Federal University |
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| Keywords | functionally constrained disturbances full-memory control strategies optimal guaranteed result quasi-strategies |
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| References_xml | – reference: ChistyakovS. V.On solving pursuit game problemsJ. Appl. Math. Mech.197741584585210.1016/0021-8928(77)90167-8519735 – reference: PetrosyanL. A.ChistyakovS. V.An approach to the solution of pursuit gamesVest. Leningr. Gos. Univ., Ser. Mat. Mekh. Astron.197717782 – reference: KrasovskiiN. N.Tret’yakovV. E.Stochastic program synthesis for a positional differential gameDokl. Akad. Nauk SSSR198125912427625396 – reference: NatansonI. P.Theory of Functions of a Real Variable1974 – reference: KrasovskiiA. N.KrasovskiiN. N.Control under Lack of Information199510.1007/978-1-4612-2568-3 – reference: KrasovskiiN. N.SubbotinA. I.Positional Differential Games19740298.90067 – reference: SerkovD. A.Synthesis of optimal control under an Lp-compact disturbanceProceedings of the 12th All-Russia Meeting on Control Problems, Moscow, Russia, 20142014MoscowInst. Probl. Upravl.688699 – reference: LukoyanovN. Yu.The problem of computing the value of a differential game for a positional functionalJ. Appl. Math. Mech.199862217718610.1016/S0021-8928(98)00023-91680636 – reference: SubbotinA. I.ChentsovA. G.Guarantee Optimization in Control Problems19810542.90106 – reference: KrasovskiiN. N.Control of a Dynamical System1985 – reference: SerkovD. A.Optimization of guaranteed results under functional restrictions on the dynamic disturbanceDokl. Math.201387331031310.1134/S106456241303011331144901277.49029 – reference: WargaJ.Optimal Control of Differential and Functional Equations19720253.49001 – reference: SerkovD. A.Optimal control under constraints on the disturbance that are compact in LpVestn. Udmurt. Univ., Ser. Mat. Mekh. Komp. Nauki201337987 – reference: KrasovskiiN. N.Game Problems on the Encounter of Motions19700246.90060 – reference: ChentsovA. G.On a game problem of converging at a given instant of timeMath. USSR-Sb.197628335337610.1070/SM1976v028n03ABEH001657 – reference: UkhobotovV. I.Construction of a stable bridge for a class of linear gamesJ. Appl. Math. Mech.197741235836110.1016/0021-8928(77)90021-1496779 – reference: SerkovD. A.Guaranteed control under functional constraints on the distrubanceMat. Teor. Igr. Prilozh.20124271951273.93114 – reference: KryazhimskiiA. V.The problem of optimization of the ensured result: Unimprovability of full-memory strategiesConstantin Carathéodory: An International Tribute1991163667510.1142/9789814350921_00371130862 – reference: GomoyunovM. I.KornevD. V.On calculating the value of a differential game in the class of counterstrategiesTrudy Inst. Mat. Mekh. UrO RAN20131915968 – volume: 259 start-page: 24 issue: 1 year: 1981 ident: 6972_CR13 publication-title: Dokl. Akad. Nauk SSSR – volume: 1 start-page: 77 year: 1977 ident: 6972_CR10 publication-title: Vest. Leningr. Gos. Univ., Ser. Mat. Mekh. Astron. – volume-title: Theory of Functions of a Real Variable year: 1974 ident: 6972_CR18 – volume-title: Optimal Control of Differential and Functional Equations year: 1972 ident: 6972_CR8 – volume: 19 start-page: 59 issue: 1 year: 2013 ident: 6972_CR16 publication-title: Trudy Inst. Mat. Mekh. UrO RAN – volume: 28 start-page: 353 issue: 3 year: 1976 ident: 6972_CR9 publication-title: Math. USSR-Sb. doi: 10.1070/SM1976v028n03ABEH001657 – volume-title: Positional Differential Games year: 1974 ident: 6972_CR2 – volume-title: Control under Lack of Information year: 1995 ident: 6972_CR14 doi: 10.1007/978-1-4612-2568-3 – volume-title: Guarantee Optimization in Control Problems year: 1981 ident: 6972_CR4 – start-page: 688 volume-title: Proceedings of the 12th All-Russia Meeting on Control Problems, Moscow, Russia, 2014 year: 2014 ident: 6972_CR17 – volume-title: Control of a Dynamical System year: 1985 ident: 6972_CR3 – volume: 41 start-page: 358 issue: 2 year: 1977 ident: 6972_CR12 publication-title: J. Appl. Math. Mech. doi: 10.1016/0021-8928(77)90021-1 – volume: 87 start-page: 310 issue: 3 year: 2013 ident: 6972_CR6 publication-title: Dokl. Math. doi: 10.1134/S1064562413030113 – volume: 4 start-page: 71 issue: 2 year: 2012 ident: 6972_CR19 publication-title: Mat. Teor. Igr. Prilozh. – volume: 41 start-page: 845 issue: 5 year: 1977 ident: 6972_CR11 publication-title: J. Appl. Math. Mech. doi: 10.1016/0021-8928(77)90167-8 – volume: 3 start-page: 79 year: 2013 ident: 6972_CR7 publication-title: Vestn. Udmurt. Univ., Ser. Mat. Mekh. Komp. Nauki doi: 10.20537/vm130307 – volume-title: Game Problems on the Encounter of Motions year: 1970 ident: 6972_CR1 – volume: 1 start-page: 636 year: 1991 ident: 6972_CR5 publication-title: Constantin Carathéodory: An International Tribute doi: 10.1142/9789814350921_0037 – volume: 62 start-page: 177 issue: 2 year: 1998 ident: 6972_CR15 publication-title: J. Appl. Math. Mech. doi: 10.1016/S0021-8928(98)00023-9 |
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| Title | On the unimprovability of full-memory strategies in problems of guaranteed result optimization |
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