The reconstruction of feedback using observation data

Abstract

The problem of the restoration of an a priori unknown feedback which operates in a dynamical controlled system is considered. The restoration is achieved using results of observations during the motion of this system and approximate measurements of its actual phase positions. It is well known that this is an ill-posed problem. Two methods are proposed for solving it: a static method and a dynamic method. When solving the problem using the static method, the results of approximate measurements of the actual phase positions of the system in any given time interval serve as the input information. Here, restoration is achieved “a posteriori” when the corresponding time interval for the observation of the motion using the whole totality of admitted information expires. The concepts of the theory of preset control and the theory of ill-posed problems are invoked to solve the problem by this method. When the problem is solved by the dynamic method, the results of instantaneous approximate measurements of the actual phase positions of the system, which proceed to the observer in the dynamics during some specified time interval, serve as the input information for the solution. Here, the measurements and restoration are achieved in the dynamics over the course of the process using the real-time information. Concepts of the theory of positional control and the theory of dynamic regularization are invoked by the dynamic method. Constructive, stable, regularizing algorithms are built in order to solve the restoration problem by this as well as by the other method. Moreover, the dynamic algorithms are physically feasible and are capable of working under realtime conditions, processing the information which is being received during the course of the motion of the system and feeding the result into the dynamics as the motion develops.