10th U6+ Consortium of African Universities International Conference

In this paper, we formulated a mathematical model using the concept of optimal control, where the state of the system is governed by a differential equation controlled by two combatants (combatant A and combatant B) refer to as the evader and pursuer respectively, with conflicting motives. A control u(.) defines a notion where the combatant A tries to escape capture from the combatant B defined by control v(.). The game terminates if capture occurs prior to a pre-assigned time t or at a time t. In a situation where capture has not occurred prior to t, the control u(.) sole-aim would be to escape capture, while combatant B sole-aim is to ensure that combatant A is captured. The sole aim of the Combatant B (the pursuer) is to make capture possible by minimizing the terminal miss as minimum as possible, and Combatant B (the evader) sole aim is to maximize the terminal miss to make capture invariably impossible.