Discontinuous control in problem of disturbance reduction for a linear dynamical system

Abstract

In the paper, we study the problem of active reduction of the influence of a disturbance on the output of a linear controlled system. The problem is investigated on infinite time intervals. We consider a system of linear differential equations under the action of an unknown disturbance and a control to be formed. Our goal is to design an algorithm for reducing the disturbance by means of an appropriate control on the basis of inaccurate measurements of all (or a part of) phase coordinates of the system. This algorithm should form a feedback control that would guarantee that the trajectory of the given system and the velocity of its changing track the trajectory and the velocity of its changing of some reference system. We present two algorithms for solving this problem. These algorithms forming piece‐wise constant controls are based on the combination of constructions of the theory of dynamical inversion and the theory of feedback control. They are stable with respect to informational noises and computational errors.