On one algorithm of the dynamical reconstruction of the right-hand side of a parabolic equation

We consider a parabolic equation with an unknown right-hand side. The problem of constructing an algorithm for the dynamical reconstruction of the unknown perturbation from the results of inaccurate state measurements is discussed. The problem belongs to the class of inverse problems, the desired algorithm being an algorithm of stable dynamic inversion (dynamic regularization). The existing algorithms of dynamical reconstruction of the right-hand sides of systems with distributed parameters are based on a combination of the positional control method and regularization methods. These algorithms are aimed at reconstructing perturbations over a bounded time segment. Computational and measurement errors accumulate as the time segment grows. In the present article we suggest a dynamical inversion algorithm that is free from this defect.