Real-time reachable set estimation for linear time-delay systems based on zonotopes

Li, Tuochen; Zheng, Cunxi; Feng, Zhiguang; Dinh, Thach Ngoc; Raïssi, Tarek

doi:10.1080/00207721.2023.2189534

Cited by 5 publications

(1 citation statement)

References 36 publications

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“…More recently, Zhang et al investigated the reachable set estimation for uncertain nonlinear systems with time delay [27]. For more references and recent advances in reachable set estimation, one can refer to [29][30][31][32]. The key point of the reachable set estimation is the choice of Lyapunov functional.…”

Section: Introductionmentioning

confidence: 99%

Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances

Jiang,

Yang,

Ivanov

2024

Mathematics

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This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control systems with bounded disturbances. By constructing an appropriate Lyapunov–Krasovskii functional, we obtain a delay-dependent condition, which determines the admissible bounding ellipsoid for the reachable set of the system we considered. Then, a sufficient condition in the form of liner matrix inequalities is given to solve the problem of controller design and reachable set estimation. Then, by minimizing the volume of the ellipsoid and solving the liner matrix inequality, we obtain the desired ellipsoid and controller gain. A comparative numerical example is given to show the effectiveness of our result.

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Section: Introductionmentioning

confidence: 99%

Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances

Jiang,

Yang,

Ivanov

2024

Mathematics

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Set‐membership state estimation for delayed switched systems with interval uncertainty: A zonotopic approach

Zhou,

Chen,

et al. 2024

Adaptive Control & Signal

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SummaryConsidering the existence of time delay and interval uncertainty, a set‐membership state estimation problem based on zonotopes is studied for discrete‐time switched systems subject to unknown but bounded noises. To conform the actual situation, a state observer asynchronous with the subsystem is designed. The performance is introduced to attenuate the effect of noises in the observer design. By dealing with the interval uncertainty, the design approach of observer is given and transformed into a convex optimization problem which can be solved off‐line. The zonotope and the estimation interval containing state are provided based on the observer. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm.

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Tight interval state estimate for discrete‐time descriptor linear systems

Lamouchi,

Meslem,

Raïssi

2024

Intl J Robust & Nonlinear

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SummaryIn this work, two state estimation methods are proposed for a class of discrete‐time descriptor linear systems subject to bounded uncertainties. First, we propose set‐valued estimator algorithm using symmetric boxes to compute rigorous bounds of the system states. The observer gains are calculated using norm to attenuate the effects of the uncertainties and to improve the accuracy of the proposed estimator. Second, to obtain tighter state enclosures, zonotopic set computation are developed instead of interval analysis to design a new set‐valued state estimation algorithm. The performances of the proposed state estimation approaches are highlighted on different illustrative examples.

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Real-time reachable set estimation for linear time-delay systems based on zonotopes

Cited by 5 publications

References 36 publications

Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances

Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances

Set‐membership state estimation for delayed switched systems with interval uncertainty: A zonotopic approach

Tight interval state estimate for discrete‐time descriptor linear systems

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