TY - JOUR

T1 - On Linear-Quadratic Differential Games for Fractional-Order Systems

AU - Gomoyunov, M.

AU - Lukoyanov, N.

N1 - This work was supported by the Russian Science Foundation, project no. 21-71-10070, https://rscf.ru/en/project/21-71-10070/.

PY - 2023

Y1 - 2023

N2 - 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 the players’ control are to minimize and maximize a quadratic terminal-integral cost function, respectively. 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 results are based on the construction of a solution to an appropriate Hamilton–Jacobi equation with fractional coinvariant derivatives under a natural right-end boundary condition. © Pleiades Publishing, Ltd. 2023. ISSN 1064-5624, Doklady Mathematics, 2023, Vol. 108, Suppl. 1, pp. S122–S127. Pleiades Publishing, Ltd., 2023. Russian Text The Author(s), 2023, published in Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2023, Vol. 15, No. 2, pp. 18–32.

AB - 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 the players’ control are to minimize and maximize a quadratic terminal-integral cost function, respectively. 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 results are based on the construction of a solution to an appropriate Hamilton–Jacobi equation with fractional coinvariant derivatives under a natural right-end boundary condition. © Pleiades Publishing, Ltd. 2023. ISSN 1064-5624, Doklady Mathematics, 2023, Vol. 108, Suppl. 1, pp. S122–S127. Pleiades Publishing, Ltd., 2023. Russian Text The Author(s), 2023, published in Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2023, Vol. 15, No. 2, pp. 18–32.

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U2 - 10.1134/S1064562423600689

DO - 10.1134/S1064562423600689

M3 - Article

VL - 108

SP - S122-S127

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - S1

ER -