Geodesic
Quasistrategies in an abstract guidance control problem
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2008), pp. 55-69

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We consider an abstract guidance control problem with elements of uncertainty, where the control procedures are identified with set-valued quasistrategies. The goal of the control consists in the guidance to the goal set under phase constraints. We construct the solvability set by the method of programmed iterations which is well known in the theory of differential games. We prove that the limit of the iterative procedure has the sense of the set of positional absorption (the stable bridge) introduced by N. N. Krasovskii. This limit coincides with the solvability set in the class of quasistrategies.
Keywords: set-valued quasistrategy, method of programmed iterations, the problem of confinement, operator of programmed absorption. 
@article{IVM_2008_10_a6,
     author = {A. G. Chentsov},
     title = {Quasistrategies in an abstract guidance control problem},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {55--69},
     publisher = {mathdoc},
     number = {10},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_10_a6/}
}
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A. G. Chentsov. Quasistrategies in an abstract guidance control problem. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2008), pp. 55-69. http://geodesic.mathdoc.fr/item/IVM_2008_10_a6/