Geodesic
Nonlinear positional differential game in the class of mixed strategies
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical control theory and differential equations, Tome 277 (2012), pp. 144-151

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The feedback control problem is considered for a nonlinear dynamic system under lack of information on disturbances. The problem on minmax-maxmin of the guaranteed result for a given positional quality index is formalized as an antagonistic two-player differential game in the framework of the concept developed in the Sverdlovsk (now Yekaterinburg) school on the theory of differential games. The problem is solved in the class of mixed strategies. The existence of the value of the game and a saddle point is established. The solution to the problem is based on the application of appropriate leader models, the method of extremal shift to the accompanying points and the method of upper convex hulls. The results of the study are applied to a realistic control model. The simulation outputs are presented. 
@article{TM_2012_277_a8,
     author = {A. A. Krasovskii and A. N. Krasovskii},
     title = {Nonlinear positional differential game in the class of mixed strategies},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {144--151},
     publisher = {mathdoc},
     volume = {277},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_277_a8/}
}
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A. A. Krasovskii; A. N. Krasovskii. Nonlinear positional differential game in the class of mixed strategies. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical control theory and differential equations, Tome 277 (2012), pp. 144-151. http://geodesic.mathdoc.fr/item/TM_2012_277_a8/