arXiv subjects

Alexey Peregudin

Publications and source records attributed to Alexey Peregudin.

4 recordsLinked to original sources

arXiv2025

Optimal Control for Minimizing Inescapable Ellipsoids in Linear Periodically Time-Varying Systems Under Bounded Disturbances

This letter addresses optimal controller design for periodic linear time-varying systems under unknown-but-bounded disturbances. We introduce differential Lyapunov-type equations to describe time-varying inescapable ellipsoids and define an integral-based measure of their size. To minimize this measure, we develop a differential Riccati equation-based approach that provides exact solutions for state-feedback, observer synthesis, and output-feedback control. A key component is a systematic procedure for determining the optimal time-varying parameter, reducing an infinite-dimensional optimization to a simple iterative process. A numerical example validates the method's effectiveness.

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arXiv2024

Optimal Control for Discrete-Time Systems under Bounded Disturbances

This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly observable sets. We provide exact solutions for state-feedback control and filtering problems, aligning with existing methods while offering improved computational efficiency. Moreover, our main contribution is the optimal solution to the output-feedback control problem for discrete-time systems which was not known before. Numerical simulations demonstrate the superiority of this result over previous sub-optimal ones.

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arXiv2023

New Dualities in Linear Systems and Optimal Output Control under Bounded Disturbances

In this paper, we introduce novel equations that are dual to the ones of the well-known invariant ellipsoids method. These equations yield ellipsoids with newly established geometrical interpretations and connections to linear system norms. The established duality leads to the optimal synthesis results for state-feedback control, filtering, and output-feedback control problems in the presence of bounded disturbances. The proposed output-feedback control solution is demonstrated to be optimal and surpass prior sub-optimal results.

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arXiv2021

Method of Attractive Cylinders. Solution for a General Linear Tracking Problem

The paper presents the method of attractive cylinders -- a generalization of the atrractive ellipsoid method to the cases of tracking and observation. Based on the developed method, an algorithm for calculating the parameters of the controller, which ensures the boundedness of tracking or observation errors in the presence of bounded external disturbances, is proposed. The effectiveness of the proposed method is demonstrated by examples.

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