The problem of dynamical reconstruction of Dirichlet boundary control in semilinear hyperbolic equations (Q2712500)

The identification problem of dynamical reconstruction of an unknown boundary control for a semilinear hyperbolic equation is considered. This problem belongs to the class of ill-posed problems. The evolution of phase states is determined by a fixed, but unknown, input (control) belonging to a given set of admissible function. Some sensors perform inaccurate measurements of phase states at discrete time moments. The authors present a regularization algorithm based on a theory of positional control in combination with methods of smoothing functional and discrepancy, which are well-known in theory of ill-posed problems.