Boundary control of a hyperbolic system with one space variable

We consider a mixed problem in a half-strip for a hyperbolic system with one space variable and with constant coefficients. The control problem is to find boundary conditions ensuring that the system has a given state vector at a given instant of time. We study whether the problem is asymptotically solvable, i.e., whether there exists a sequence of boundary conditions such that the corresponding sequence of final state vectors uniformly converges to the given vector. We reduce the construction of a family of such sequences of boundary conditions with a function parameter to the solution of a Fredholm integral equation of the second kind and prove a sufficient condition for its unique solvability in terms of the problem data.