Geodesic
On Hamilton--Jacobi--Isaacs--Bellman equation for neutral type systems
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 2, pp. 222-237

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For a conflict-controlled dynamical system described by functional differential equations of neutral type in Hale’s form, we consider a differential game with a quality index that estimates the motion history realized up to the terminal time and includes an integral estimation of realizations of players’ controls. The game is formalized in the class of pure positional strategies. Based on a coinvariant derivatives conception we derive a Hamilton–Jacobi functional equation. It is proved, firstly, that the solution of this equation, satisfying certain conditions of smoothness, is the value of the initial differential game, and secondly, that value at points of differentiability satisfies the considered Hamilton–Jacobi equation. Thus this equation can be interpreted as the Hamilton–Jacobi–Isaacs–Bellman equation for neutral type systems.
Keywords: neutral type systems, differential games, Hamilton–Jacobi equation. 
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     author = {A. R. Plaksin},
     title = {On {Hamilton--Jacobi--Isaacs--Bellman} equation for neutral type systems},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {222--237},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2017_27_2_a5/}
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A. R. Plaksin. On Hamilton--Jacobi--Isaacs--Bellman equation for neutral type systems. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 2, pp. 222-237. http://geodesic.mathdoc.fr/item/VUU_2017_27_2_a5/