Optimal pursuit time for a differential game in the Hilbert space l2

Abstract

We consider a two-person zero-sum pursuit-evasion differential game in the Hilbert space l2. The control functions of the players are subject to integral constraints. It is assumed that the control resource of the pursuer is greater than that of the evader. The pursuer tries to force the state of the system towards the origin of the space l2, and the evader tries to avoid this. We give a solution to the optimal pursuit problem for the differential game. More precisely, we obtain an equation for the optimal pursuit time and construct optimal strategies for the players in an explicit form. To prove the main result we solve a time-optimal control problem.

On the stability and null-controllability of an infinite system of linear differential equations

“…To prove item (i) we look for the set of y 0 ∈ ℓ 2 with y 0 2 2 ≤ κρ 2 . Then by (18) we have that y(τ ) = 0 for the solution started from y 0 . Also, by (19) and the choice of y 0 the function f 0 defined by ( 17) is admissible.…”

“…A considerable amount of work devoted to differential game problems for infinite systems in Hilbert spaces (see for example [16,17] and references therein). Optimal strategies for players in suitable classes of strategies have been constructed in [18].…”

The solution of an infinite system of ternary differential equations

“…., in (4) are any real numbers. Later on various differential game problems described for infinite systems of differential equations were studied in the works [15][16][17][18][19].…”

Differential Game With a Lifeline for the Inertial Movements of Players

“…The main technique for solving the pursuit and evasion problems is constructing optimal strategies of players and defining the value of the game. The works [16][17][18][19]21] are devoted to studying differential games of simple motion and by optimal strategies of players, it was proved that the value of the game exists.…”