Geodesic
On linear differential games with convex integral constraints
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 4, pp. 308-319

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We consider the problem of the approach of a trajectory of a linear conflict-controlled process to a linear subspace in the case of general integral constraints on the player's controls. Using the technique of set-valued mappings and convex analysis (epigraph of a function, recession cone), we obtain sufficient conditions for problem solvability in the class of measurable controls. The relation to a dual description based on conjugate functions is specified. Termination conditions for a game with impulse controls are established. The results are exemplified by means of model problems with various types of constraints on the players' controls.
Keywords: differential game, integral constrains, set-valued mapping, recession cone, impulse control. 
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     author = {A. A. Chikrii and A. A. Belousov},
     title = {On linear differential games with convex integral constraints},
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     publisher = {mathdoc},
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     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_4_a29/}
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A. A. Chikrii; A. A. Belousov. On linear differential games with convex integral constraints. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 4, pp. 308-319. http://geodesic.mathdoc.fr/item/TIMM_2013_19_4_a29/