Tracking the Solution of a Linear Parabolic Equation Using Feedback Laws

We consider the problem of tracking the solution of a parabolic equation with an unknown right-hand side by the solution of a similar parabolic equation. To solve this problem, we propose two noise-resistant algorithms based on the extremal shift method known in guaranteed control theory. The first algorithm pertains to the case of continuous measurement of solutions to the equations, and the second, to the case of discrete measurement.