Geodesic
On linear-quadratic differential games for fractional-order systems
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 15 (2023) no. 2, pp. 18-32

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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. 
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     author = {Mikhail I. Gomoyunov and Nikolai Yu. Lukoyanov},
     title = {On linear-quadratic differential games for fractional-order systems},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {18--32},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2023_15_2_a1/}
}
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Mikhail I. Gomoyunov; Nikolai Yu. Lukoyanov. On linear-quadratic differential games for fractional-order systems. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 15 (2023) no. 2, pp. 18-32. http://geodesic.mathdoc.fr/item/MGTA_2023_15_2_a1/