Geodesic
A game-control problem under lack of information
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 4 (2012) no. 2, pp. 57-70

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The optimal feedback control problem is considered for the nonlinear dynamical system under lack of information on disturbances. The minimax-maximin problem on the guaranteed result for a given positional quality index is formalized in the framework of concepts of the Sverdlovsk-Ekaterinburg school on the theory of differential games, as the two-person antagonistic differential game. The existence of a saddle point and a value of the game is obtained. The solution of a problem is based on the method of extremal shift to accompanying points. Results are illustrated by the model example and its numerical simulation.
Keywords: nonlinear dynamical system, control, disturbance, quality index, guaranteed result, extremal shift, value of the game, saddle point. 
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     author = {Andrew N. Krasovskii and Alexandr N. Ladeyschikov},
     title = {A game-control problem under lack of information},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
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     volume = {4},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2012_4_2_a3/}
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Andrew N. Krasovskii; Alexandr N. Ladeyschikov. A game-control problem under lack of information. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 4 (2012) no. 2, pp. 57-70. http://geodesic.mathdoc.fr/item/MGTA_2012_4_2_a3/