Control of dynamic systems under information deficit. Guaranteed approach. I. Estimation algorithms

V. I. Shiryaev

South Ural State University, Chelyabinsk

Abstract: In this paper, we consider the problems of synthesis of positional control for linear dynamic systems in the case where it is necessary to guarantee the achievement of the control goal, and the disturbances acting on the dynamic system and the interference in the information channels of the system are known with an accuracy of sets in which they can take any values. We construct information sets and forecast sets that contain the state vector. Control problems are solved for the case of specifying requirements for the system in the form of sets in the phase space to which the state vector must belong, taking into account the constraints on control, or with requirements in the form of a quadratic functional. The application of Lyapunov functions for control synthesis is shown. The first part of this work is devoted to evaluation algorithms.

Keywords: dynamic system, control, estimation, disturbance uncertainty, noise, information set, forecast, Lyapunov function

UDC: 519.714, 517.977

MSC: 34Cxx, 70Cxx

DOI: 10.36535/2782-4438-2025-243-90-112