Linear Pursuit Differential Game under Phase Constraint on the State of Evader

We consider a linear pursuit differential game of one pursuer and one evader. Controls of the pursuer and evader are subjected to integral and geometric constraints, respectively. In addition, phase constraint is imposed on the state of evader, whereas pursuer moves throughout the space. We say that pursuit is completed, if inclusion y ( t 1 ) − x ( t 1 ) ∈ M is satisfied at some t 1 > 0, where x ( t ) and y ( t ) are states of pursuer and evader, respectively, and M is terminal set. Conditions of completion of pursuit in the game from all initial points of players are obtained. Strategy of the pursuer is constructed so that the phase vector of the pursuer first is brought to a given set, and then pursuit is completed.

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