LINEAR PURSUIT GAMES ON TIME SCALES WITH DELAY IN INFORMATION AND GEOMETRICAL CONSTRAINTS

Abstract

The time scales that enable the integration of the dynamics equations presented by differential equations and difference equations under the same model are the dynamic equations on time scales, and many other models are expressed by the dynamic equations on time scales as well. The pursuit problem is a basic problem of games theory, in which, the motions of two given objects (the pursuer and the evader) are described by the differential equations involved in the control variables. In this problem, the pursuer shall construct their control  according to the information of the evader. And in reality, the information constructed by the pursuer is usually delayed for a certain amount of time. The paper considers some sufficient conditions for completing the linear pursuit games with delay in information. The controls of the pursuer and the evader are impacted by the geometrical constraints.