On dynamical reconstruction of an unknown input in the parabolic obstacle problem
A problem of dynamical reconstruction of a control for a parabolic obstacle problem is considered. A solving algorithm for this problem is presented. This algorithm is stable with respect to informational noise and computational errors. It adaptively takes into account inaccurate measurements of phase trajectories and is regularizing in the sense that the final result becomes better as the input information becomes more accurate. The algorithm suggested in the paper is based on the theory of positional control. The main element of this algorithm is a procedure of stabilizing some auxiliary functionals of the Lyapunov type.