Modified Resolving-Functions Method for Game Problems of Approach of Controlled Objects with Different Inertia

The problem of the approach of controlled objects with different inertia in dynamic game problems is considered. Modified sufficient conditions for ending the game in a finite guaranteed time when Pontryagin’s condition is not satisfied are formulated. Some shift functions are considered instead of...

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Vydané v:	Cybernetics and systems analysis Ročník 59; číslo 2; s. 251 - 265
Hlavní autori:	Chikrii, A. A., Rappoport, I. S.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.03.2023 Springer Springer Nature B.V
Predmet:	Artificial Intelligence Control Cybernetics Games Inertia Mathematics Mathematics and Statistics Processor Architectures Software Engineering/Programming and Operating Systems Systems Theory quasi-linear differential game resolving function multi-valued mapping stroboscopic strategy controlled objects with different inertia measurable selector
ISSN:	1060-0396, 1573-8337
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Abstract	The problem of the approach of controlled objects with different inertia in dynamic game problems is considered. Modified sufficient conditions for ending the game in a finite guaranteed time when Pontryagin’s condition is not satisfied are formulated. Some shift functions are considered instead of the Pontryagin selector, and special multi-valued mappings are introduced with their help. They generate the upper and lower resolving functions of a special type, and based on them, two types of modified schemes are proposed: the scheme of Pontryagin’s first method and the method of resolving functions. This ensures the completion of the conflict-controlled process for objects with different inertia in the class of quasi-strategies and counter-controls. New theoretical results are illustrated by a model example.
AbstractList	The problem of the approach of controlled objects with different inertia in dynamic game problems is considered. Modified sufficient conditions for ending the game in a finite guaranteed time when Pontryagin’s condition is not satisfied are formulated. Some shift functions are considered instead of the Pontryagin selector, and special multi-valued mappings are introduced with their help. They generate the upper and lower resolving functions of a special type, and based on them, two types of modified schemes are proposed: the scheme of Pontryagin’s first method and the method of resolving functions. This ensures the completion of the conflict-controlled process for objects with different inertia in the class of quasi-strategies and counter-controls. New theoretical results are illustrated by a model example. The problem of the approach of controlled objects with different inertia in dynamic game problems is considered. Modified sufficient conditions for ending the game in a finite guaranteed time when Pontryagin's condition is not satisfied are formulated. Some shift functions are considered instead of the Pontryagin selector, and special multi-valued mappings are introduced with their help. They generate the upper and lower resolving functions of a special type, and based on them, two types of modified schemes are proposed: the scheme of Pontryagin's first method and the method of resolving functions. This ensures the completion of the conflict- controlled process for objects with different inertia in the class of quasi-strategies and counter- controls. New theoretical results are illustrated by a model example. Keywords: controlled objects with different inertia, quasi-linear differential game, multi-valued mapping, measurable selector, stroboscopic strategy, resolving function.
Audience	Academic
Author	Chikrii, A. A. Rappoport, I. S.
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References_xml	– reference: 2. A. A. Chikrii, Conflict Controlled Processes, Springer Sci. and Business Media, Boston–London–Dordrecht (2013). – reference: ChikriiAARappoportISMethod of resolving functions in the theory of conflict-controlled processesCybern. Syst. Analysis2012484512531322832210.1007/s10559-012-9430-y1311.91038 – reference: KrasovskiiNNSubbotinAIPositional Differential Games1974MoscowNauka0298.90067[in Russian] – reference: 1. L. S. Pontryagin, Selected Scientific Works, Vol. 2 [in Russian], Nauka, Moscow (1988). – reference: 4. A. A. Chikrii and V. K. Chikrii, “Image structure of multivalued mappings in game problems of motion control,” J. Autom. Inform. Sci., Vol. 48, Iss. 3, 20–35 (2016). – reference: IoffeADTikhomirovVMTheory of Extremum Problems1974MoscowNauka[in Russian] – reference: SubbotinAIChentsovAGGuarantee Optimization in Control Problems1981MoscowNauka0542.90106[in Russian] – reference: RappoportISMethod of resolving functions for game problems of approach of controlled objects with different inertiaCybern. Syst. Analysis202157229631210.1007/s10559-021-00355-91470.91045 – reference: HajekOPursuit Games1975New YorkAcad. Press0324.90104 – reference: 9. J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhauser, Boston–Basel–Berlin (1990). – reference: RockafellarRTConvex Analysis1970PrincetonPrinceton Univ. Press10.1515/97814008731730193.18401 – reference: ChikriiAAAn analytical method in dynamic pursuit gamesProc. Steklov Inst. of Mathematics20102716985284171310.1134/S00815438100400731302.49052 – ident: 559_CR4 doi: 10.1615/JAutomatInfScien.v48.i3.30 – volume: 48 start-page: 512 issue: 4 year: 2012 ident: 559_CR12 publication-title: Cybern. Syst. Analysis doi: 10.1007/s10559-012-9430-y – volume: 57 start-page: 296 issue: 2 year: 2021 ident: 559_CR5 publication-title: Cybern. Syst. Analysis doi: 10.1007/s10559-021-00355-9 – volume-title: Theory of Extremum Problems year: 1974 ident: 559_CR11 – volume-title: Convex Analysis year: 1970 ident: 559_CR10 doi: 10.1515/9781400873173 – volume-title: Positional Differential Games year: 1974 ident: 559_CR6 – volume: 271 start-page: 69 year: 2010 ident: 559_CR3 publication-title: Proc. Steklov Inst. of Mathematics doi: 10.1134/S0081543810040073 – ident: 559_CR9 – volume-title: Guarantee Optimization in Control Problems year: 1981 ident: 559_CR7 – volume-title: Pursuit Games year: 1975 ident: 559_CR8 – ident: 559_CR1 – ident: 559_CR2
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