Integral equations method for a vector inverse problem

The paper discusses a dynamic system described by a system of linear differential equations. In many cases, instead of the true signal, which is perceived by the measuring device, a distorted signal is observed at the output, which significantly differs in structure, magnitude, and time parameters from the true one. Such distortions are generated by the operation principles of the measuring device, noise or interference contained in the input signal, and distortions arising from the operation of the device itself. Under these conditions, one of the problems of significant interest for applications is the inverse problem, restoring the input signal from the available information (including indirect information) about the signal at the output of the system and estimating the accuracy of the solutions obtained. The paper proposes a method of integral equations and its numerical implementation, which make it possible to effectively restore the input action on a dynamic system from indirect experimental information.