Geodesic
Stable Functionals of Neutral-Type Dynamical Systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control and differential equations, Tome 304 (2019), pp. 221-234

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We consider a controlled dynamical system under noisy conditions. Its motion is described by functional differential equations of neutral type in the form of J. Hale. A functional of the motion history is said to be stable with respect to this system if there exists a control strategy that guarantees the monotonicity of this functional for any noise. We study various nonlocal and infinitesimal conditions for the stability of functionals.
Keywords: differential games optimal control, coinvariant derivatives, directional derivatives, Hamilton–Jacobi equations, stable functionals. 
@article{TM_2019_304_a13,
     author = {N. Yu. Lukoyanov and A. R. Plaksin},
     title = {Stable {Functionals} of {Neutral-Type} {Dynamical} {Systems}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {221--234},
     publisher = {mathdoc},
     volume = {304},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2019_304_a13/}
}
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N. Yu. Lukoyanov; A. R. Plaksin. Stable Functionals of Neutral-Type Dynamical Systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal control and differential equations, Tome 304 (2019), pp. 221-234. http://geodesic.mathdoc.fr/item/TM_2019_304_a13/