RUS  ENG
Full version
JOURNALS // Matematicheskaya Teoriya Igr i Ee Prilozheniya // Archive

Mat. Teor. Igr Pril., 2023 Volume 15, Issue 2, Pages 18–32 (Mi mgta321)

This article is cited in 2 papers

On linear-quadratic differential games for fractional-order systems

Mikhail I. Gomoyunovab, Nikolai Yu. Lukoyanovba

a N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of RAS
b Ural Federal University

Abstract: We consider a finite-horizon two-person zero-sum differential game in which the system dynamics is described by a linear differential equation with a Caputo fractional derivative and the goals of control of the players are, respectively, to minimize and maximize a quadratic terminal-integral cost function. We present conditions for the existence of a game value and obtain formulas for players' optimal feedback control strategies with memory of motion history. The basis of the results is the construction of a solution of the appropriate Hamilton – Jacobi equation with so-called fractional coinvariant derivatives under a natural right-end boundary condition.

Keywords: linear-quadratic differential game, fractional-order system, game value, optimal strategies, Hamilton – Jacobi equation.

UDC: 517.977.8
BBK: 22.18

Received: 17.04.2023
Revised: 01.05.2023
Accepted: 15.05.2023



© Steklov Math. Inst. of RAS, 2025