Linear evasion differential game of one evader and several pursuers with integral constraints

An evasion differential game of one evader and many pursuers is studied. The dynamics of state variables x1, … , xm are described by linear differential equations. The control functions of players are subjected to integral constraints. If xi(t) ≠ 0 for all i∈ { 1 , … , m} and t≥ 0 , then we say that evasion is possible. It is assumed that the total energy of pursuers doesn’t exceed the energy of evader. We construct an evasion strategy and prove that for any positive integer m evasion is possible.