A linear group pursuit problem with fractional derivatives and different player capabilities

Abstract

In a finite-dimensional Euclidean space, the problem of pursuit of one evader by a group of pursuers is considered, described by a system of the form $$ D^{(\alpha)}x_i = a_i x_i + u_i, \ u_i \in U_i,\quad D^{(\alpha)}y = ay + v, \ v \in V, $$ where $D^{(\alpha)}f$ is the Caputo derivative of order $\alpha \in (1, 2)$ of the function $f$. Sets of admissible controls~$U_i$, $V$ are convex compacts, $a_i$, $a$ are real numbers. Terminal sets are convex compacts. Sufficient conditions for the solvability of the problems of pursuit and evasion are obtained. In the study, the method of resolving functions is used as the basic one.