Geodesic
On construction of optimal synthesis in the problem of maximal viability
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2006), pp. 3-14

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The conditions for existence of optimal synthesis in the problem of maximization of time were obtained in the case when Bellman equation has solution in the class of smooth functions. One example is considered. 
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V. N. Baranov. On construction of optimal synthesis in the problem of maximal viability. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2006), pp. 3-14. http://geodesic.mathdoc.fr/item/VUU_2006_1_a0/