Differential Games in Fractional-Order Systems: Inequalities for Directional Derivatives of the Value Functional

M. I. Gomoyunov ; N. Yu. Lukoyanov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 74-94.

Résumé

For a dynamical system described by differential equations with Caputo fractional derivatives of order $\alpha \in (0,1)$, we consider a minimax–maximin differential game with a performance index that estimates the motion of the system on a fixed finite time interval. We obtain differential inequalities that characterize the value functional of the game in terms of appropriate directional derivatives.

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