Differential games with many pursuers and integral constraints on controls of players - Ali Allahabi, Fateh Abdo (2011)
Control and differential game problems, with dynamics described by parabolic and hyperbolic partial differential equations attract the attention of many researchers. Some of these problems can be reduced to the one described by infinite systems of ordinary differential equations by using the decomposition method. The main purpose of this thesis is to study the differential game problems described by an infinite system of 2-systems of second order differential equations, and it is extension to multi-player pursuit-evasion differential game problems, with various constraints, on control functions of players. The existence and uniqueness theorem in the space C(0, T; l2 r ) is proved. Built on this, an optimal control for the control system described by an infinite system of differential equations with integral constraint is presented. The optimal control result is extended to study a pursuit differential game problem with the integral constrains on the controls of players. The goal of the Pursuer is to force the system and its velocity to the origin on the spaces l2 r+1 and l2r respectively, and the Evader exactly tries to avoid this. In addition to this, a theorem on pursuit with mixed constraints is proved, where Pursuers control is subjected to integral constraint and geometric constraint is imposed on Evaders control. Moreover, we established the sufficient conditions for which evasion is possible in the game considered, with geometric constraints on the control of players. Furthermore, control of the Evader is constructed in an explicit form. Finally, a pursuit-evasion game with m Pursuer and one Evader are studied. In the pursuit game we present sufficient condition for which the Pursuers can bring the state of the system and its velocity into the origin for a finite time. For the evasion game we state and prove a theorem for which evasion is possible from any initial position