Evasion Differential Game of Multiple Pursuers and One Evader for an Infinite System of Binary Differential Equations

Abstract

We study a differential evasion game of multiple pursuers and an evader governed by several infinite systems of two-block differential equations in the Hilbert space l2. Geometric constraints are imposed on the players’ control functions. If the state of a controlled system falls into the origin of the space l2 at some finite time, then pursuit is said to be completed in a differential game. The aim of the pursuers is to transfer the state of at least one of the systems into the origin of the space l2, while the purpose of the evader is to prevent it. A sufficient evasion condition is obtained from any of the players’ initial states and an evasion strategy is constructed for the evader.

Keywords

• infinite system of differential equations
• differential game
• strategy
• control
• geometric constraint