On linear-quadratic differential games for fractional-order systems

Mikhail I. Gomoyunov ; Nikolai Yu. Lukoyanov

Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 15 (2023) no. 2, pp. 18-32.

Résumé

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.

Détail

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

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