On a Control Problem for a Linear System with Measurements of a Part of Phase Coordinates

Abstract

We consider a control problem for a system of linear ordinary differential equations. It is required to design a feedback control procedure under which the rate of change of a part of the phase coordinates of the system would track the rate of change of a part of the phase coordinates of another system subject to an unknown disturbance. It is assumed that a part of phase coordinates of each of the systems is measured with error at discrete times. We propose a solution algorithm that is stable with respect to informational noises and computation errors. The algorithm is based on the extremal shift method known in the theory of guaranteed control. Since it is impossible to apply the “classical” extremal shift due to the incompleteness of the information on the phase coordinates, we propose a modification of this method that employs elements of the dynamic inversion theory. The latter is based on constructions from the theory of ill-posed problems. In the concluding section of the paper, we specify a class of systems nonlinear in the phase coordinates for which the algorithm is applicable.