On a control problem and a pursuit game of transferring states described by an infinite three-systems of differential equations

In this paper, we devote to study a pursuit game described by an infinite three-systems of differential equations in Hilbert space. The game involves transferring of the states as the pursuit is said to be completed if the state ζ(·) of the system is shifted to another non zero state ζ1 of the system at some finite time. The control functions of the players are constrained by geometric constraints. We first find the control function that transfers the control system’s state to the state ζ1 at some time. We then extend to solve the pursuit problem where an admissible pursuer’s strategy is constructed and a guaranteed pursuit time is determined.

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