Geodesic
Stable bridge construction in games with simple motions in the plane
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 128-142

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It is known that the solvability set (the maximal stable bridge) in a zero-sum differential game with simple motions, fixed terminal time, geometric constraints on the controls of the first and second players, and convex terminal set can be constructed by means of a program absorption operator. In this case, a backward procedure for the construction of $t$-sections of the solvability set does not need any additional partition times. We establish the same property for a game with simple motions, polygonal terminal set (which is generally nonconvex), and polygonal constraints on the players's controls in the plane. In the particular case of a convex terminal set, the operator used in the article coincides with the program absorption operator.
Keywords: differential games with simple motions in the plane, solvability set, backward procedure. 
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L. V. Kamneva; V. S. Patsko. Stable bridge construction in games with simple motions in the plane. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 128-142. http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a11/