Geodesic
Guidance game problems for linear integro-differential systems of Volterra type with control action under the integral sign
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 6 (2014) no. 3, pp. 42-49

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The paper is focused on pursuit-evasion game situations for controlled dynamic objects, the development of which is described by linear integro-differential and integral systems of Volterra type with control action under the integral sign. As a result, the control system has new essential features that are not obtained by traditional controlled differential systems. The author formulates a new definition of game position, the calculation of which requires the total memory of control action in a moment of aiming. Well-known extreme constructions by an academician N. N. Krasovsky modified by the author are used to solve these problems.
Keywords: integro-differential system; guidance problem; control action; program maximin; game position. 
@article{VYURM_2014_6_3_a5,
     author = {V. L. Pasikov},
     title = {Guidance game problems for linear integro-differential systems of {Volterra} type with control action under the integral sign},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {42--49},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2014_6_3_a5/}
}
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V. L. Pasikov. Guidance game problems for linear integro-differential systems of Volterra type with control action under the integral sign. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 6 (2014) no. 3, pp. 42-49. http://geodesic.mathdoc.fr/item/VYURM_2014_6_3_a5/