RUS  ENG
Full version
JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive
Trudy Mat. Inst. Steklova, 2019 Volume 304, Pages 221–234 (Mi tm3968)
This article is cited in 6 papers

Stable Functionals of Neutral-Type Dynamical Systems

N. Yu. Lukoyanovab, A. R. Plaksinab

a N. N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620990 Russia
b Ural Federal University named after the First President of Russia B. N. Yeltsin, ul. Mira 19, Yekaterinburg, 620002 Russia

Abstract: 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.

UDC: 517.977

Received: August 2, 2018
Revised: September 20, 2018
Accepted: January 10, 2019

DOI: 10.4213/tm3968


 English version: Proceedings of the Steklov Institute of Mathematics, 2019, 304, 205–218

Bibliographic databases:

© Steklov Math. Inst. of RAS, 2024