Differential Games for an Infinite 2-Systems of Differential Equations

Abstract

A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l2. Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l2. The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.

On Stackelberg Leader with Min-Max Followers to Solve Fuzzy Continuous Static Games

“…Khalifa and Kumar [21] investigated cooperative continuous static games in a crisp environment, defining and determining the first-kind stability set corresponding to the solution without differentiability. Under uncertainty environment, some recent researchers for cooperative games have been introduced (Mallozzi and Messalli [22], Bigdeli and Hassanpour [23], Elshafei [24], Zaichenko [25], Zidan et al [26], Donahue et al [27], Ganzfried [28], Zhou et al [29], Krishankumar et al [30,31], Tukhtasinov et al [32], Sivagami et al [33], Zhao et al [34], Megahed [35], Romanuke [36], and Khalifa et al [37]).…”

Evasion Differential Game of Multiple Pursuers and One Evader for an Infinite System of Binary Differential Equations

“…For an infinite system of binary differential equations in the space l 2 , we have studied an evasion differential game problem. In [42], it has been shown that if the pursuer control set contains the evader control set, i.e., if ρ > σ, then the pursuit can be completed for a finite time. Consequently, if in game (3) ρ k > σ for some k ∈ {1, 2, .…”

“…For an infinite system of binary differential equations in the Hilbert space l 2 , the pursuit differential game of one pursuer and one evader was studied in [42], when the pursuer's control set contains the evader's control set.…”

On a Linear Differential Game of Pursuit with Integral Constraints in ℓ2

“…It remains to show that u 0 is admissible, i.e., there exists τ > 0 such that ∥u 0 ∥ ≤ ρ. For any x 0 ∈ ℓ 2 with ∥x 0 ∥ 2 2 ≤ κ 2 ρ 2 , then (17) implies that x(τ) = 0 for the solution started from x 0 . The definition of W(τ) (12) and (15)…”

“…Differential games in this setting have also been studied, with works such as [15][16][17][18][19][20] considering pursuit-evasion games for systems in infinite-dimensional phase spaces. In certain cases, optimal strategies for players were constructed within appropriate strategy classes.…”