Differential games of many players for infinite system of differential equations
This thesis focuses on studying evasion and pursuit differential games involving multiple pursuers and a single evader for infinite systems of differential equations in the Hilbert space l2. Three problems are examined in this thesis. In the first problem, an evasion differential game with multip...
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| Format: | Thesis |
| Language: | English |
| Published: |
2024
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| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/119108/ http://psasir.upm.edu.my/id/eprint/119108/1/119108.pdf |
| Summary: | This thesis focuses on studying evasion and pursuit differential games involving
multiple pursuers and a single evader for infinite systems of differential equations
in the Hilbert space l2. Three problems are examined in this thesis. In the first
problem, an evasion differential game with multiple pursuers and one evader is
considered, described by an infinite system of binary differential equations in two
cases. Solutions are presented for the evasion problem with negative coefficients in
the first case and nonnegative coefficients in the second case, under the geometric
constraints imposed on the players’ controls. The goal of the pursuers is to bring
the state of at least one controlled system to the origin of l2, while the evader aims
to prevent this. A sufficient condition for evasion is obtained for any initial state
of the players, and an evasion strategy for the evader is constructed. The second
problem involves a multiple-pursuer and single-evader evasion differential game
with integral constraints for an infinite system of two-block differential equations.
For this problem, it is shown that if the evader’s control resource is greater than
or equal to the combined resources of the pursuers, evasion is possible from any
initial position in the infinite system. Both the first and second problems are
approached by reducing the game in Hilbert space l2 to an equivalent differential
game in finite-dimensional Euclidean space. An explicit evasion strategy is proposed,
guaranteeing successful evasion. The third problem addresses a pursuit
differential game involving multiple pursuers and one evader, described by an
infinite system of second-order differential equations, where the players’ control
functions are subject to integral constraints. To solve this problem, the case of
one pursuer and one evader is first examined, and this result is subsequently applied
to obtain the main result of the problem. Additionally, a condition in terms
of the players’ energies is derived, providing a sufficient condition for successful
pursuit. Strategies for the pursuers are constructed to ensure the capture of the
evader. |
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