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Numerical Construction of Stackelberg Solutions in a Linear Positional Differential Game Based on the Method of Polyhedra

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Abstract

We consider the problem of constructing approximate Stackelberg solutions in a linear non-zero-sum positional differential game of two players with terminal payoffs and player controls chosen on convex polyhedra. A formalization of player strategies and motions generated by them is based on the formalization and results of the theory of zero-sum positional differential games developed by N.N. Krasovskii and his scientific school. The problem of finding a Stackelberg solution reduces to solving nonstandard optimal control problems. We propose an approach based on operations with convex polyhedra.

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Correspondence to D. R. Kuvshinov.

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Original Russian Text © D.R. Kuvshinov, S.I. Osipov, 2018, published in Avtomatika i Telemekhanika, 2018, No. 3, pp. 111–126.

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Kuvshinov, D.R., Osipov, S.I. Numerical Construction of Stackelberg Solutions in a Linear Positional Differential Game Based on the Method of Polyhedra. Autom Remote Control 79, 479–491 (2018). https://doi.org/10.1134/S0005117918030074

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