Geodesic
On the stability of a~procedure for solving a~minimax control problem for a~positional functional
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 68-82

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We consider a minimax feedback control problem for a linear dynamic system with a positional quality criterion, which is the norm of the family of deviations of the motion from given target points at given times. The problem is formalized as a positional differential game. A procedure for calculating the value of the game based on the backward construction of upper convex hulls of auxiliary program functions is studied. We also study a method of generating a minimax control law based on this procedure and on the extremal shift principle. The stability of the proposed resolving constructions with respect to computational and informational noises is proved.
Keywords: optimal control, differential games, stability. 
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M. I. Gomoyunov; N. Yu. Lukoyanov. On the stability of a~procedure for solving a~minimax control problem for a~positional functional. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 1, pp. 68-82. http://geodesic.mathdoc.fr/item/TIMM_2014_20_1_a6/