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Ellipsoidal Reachability Sets of Linear Time-Varying Systems in Estimation and Control Problems

Ellipsoidal Reachability Sets of Linear Time-Varying Systems in Estimation and Control Problems We consider a linear time-varying system with an initial state and disturbance that are known imprecisely and satisfy a common constraint. The constraint is the sum of a quadratic form of the initial state and the time integral of a quadratic form of the disturbance, and these quadratic forms are allowed to be degenerate. We obtain a linear matrix differential Lyapunov equation describing the evolution of the ellipsoidal reachability set. In the problem of estimating the state based on output observations, this result is used to find the minimum-size ellipsoidal set of admissible system states, which is determined by the optimal observer and by the reachability set of the corresponding observation error equation. A method for control law synthesis ensuring that the system state reaches the target set or the system trajectory remains in a given ellipsoidal tube is proposed. Illustrative examples are given for the Mathieu equation, which describes parametric oscillations of a linear oscillator. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Ellipsoidal Reachability Sets of Linear Time-Varying Systems in Estimation and Control Problems

Balandin, D.; Biryukov, R.; Kogan, M.
Differential Equations , Volume 55 (11) – Dec 17, 2019
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References (25)

Publisher
Springer Journals
Copyright
Copyright © 2019 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S00122661190110041
Publisher site
See Article on Publisher Site

Abstract

We consider a linear time-varying system with an initial state and disturbance that are known imprecisely and satisfy a common constraint. The constraint is the sum of a quadratic form of the initial state and the time integral of a quadratic form of the disturbance, and these quadratic forms are allowed to be degenerate. We obtain a linear matrix differential Lyapunov equation describing the evolution of the ellipsoidal reachability set. In the problem of estimating the state based on output observations, this result is used to find the minimum-size ellipsoidal set of admissible system states, which is determined by the optimal observer and by the reachability set of the corresponding observation error equation. A method for control law synthesis ensuring that the system state reaches the target set or the system trajectory remains in a given ellipsoidal tube is proposed. Illustrative examples are given for the Mathieu equation, which describes parametric oscillations of a linear oscillator.

Journal

Differential Equations – Springer Journals

Published: Dec 17, 2019

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