Boundary control problem for the one-dimensional Klein-Gordon-Fock equation with a variable coefficient: The case of control by displacements at two endpoints

We consider the problem of boundary control by displacements at two points x = 0 and x = l of a process described by the Klein-Gordon-Fock equation with a variable coefficient on the finite interval 0 ≤ x ≤ l . For the critical time interval T = l , we obtain a necessary and sufficient condition for the existence of unique boundary functions u (0, t ) = µ( t ) and u ( l, t ) = ν ( t ) bringing the system from an arbitrary initial state at t = 0 into an arbitrary terminal state at t = T .