On the reconstruction of inputs in linear parabolic equations

Abstract

The problem of reconstructing distributed inputs in linear parabolic equations is investigated. The algorithm proposed for solving this problem is stable with respect to informational disturbances and computational errors. It is based on the combination of methods from the theory of ill-posed problems and from the theory of positional control. The process of reconstructing unknown inputs implemented by the algorithm employs inaccurate measurements of phase coordinates of the system at discrete sufficiently frequent times. In the case when the input is a function of bounded variation, an upper estimate is established for the convergence rate.