The existence-uniqueness theorem for a system of differential equations in the spaces l2r+1

We study an infinite system of differential equations of the second order. Some special cases of the system result from application of the decomposition method to some hyperbolic equations. We discuss the existence and uniqueness questions in the space l2r+1. The proved theorem enables us to investigate some optimal control and differential game problems described by such a system

An evasion differential game described by an infinite system of 2-systems of second order.

We study a differential game of many pursuers described by infinite systems of second order ordinary differential equations. Controls of players are subjected to geometric constraints. Differential game is considered in Hilbert spaces. We say that evasion is possible if ||zi(t)||r+1 + ||z˙i(t)||r 6= 0 for all i = 1, ...,m, and t > 0; m is the number of pursuers. We proved one theorem on evasion. Moreover, we constructed explicitly a control of the evader

Evasion from one pursuer in a Hilbert space

We study a differential game of one pursuer and one evader described by infinite systems of second order ordinary differential equations. Controls of players are subjected to geometric constraints. Differential game is considered in Hilbert spaces. We proved one theorem on evasion. Moreover, we constructed explicitly a control of the evader

Solution of an infinite system of differential equations.

We consider an infinite system of differential equations of the second order. Existence and uniqueness questions are discussed in the Hilbert space. We obtain a result which enables the investigation of optimal control and differential game problems described by such a system

A pursuit problem in an infinite system of second-order differential equations

We study a pursuit differential game problem for an infinite system of second-order differential equations. The control functions of players, i.e., a pursuer and an evader are subject to integral constraints. The pursuit is completed if z(τ) = z˙ (τ) = 0 at some τ > 0, where z(t) is the state of the system. The pursuer tries to complete the pursuit and the evader tries to avoid this. A sufficient condition is obtained for completing the pursuit in the differential game when the control recourse of the pursuer is greater than the control recourse of the evader. To construct the strategy of the pursuer, we assume that the instantaneous control used by the evader is known to the pursuer

Differential games with many pursuers and integral constraints on controls of players

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 positio