A Novel Set-Theoretic Interval Observer for Discrete Linear Time-Invariant Systems

Xu, Feng; Yang, Songlin; Wang, Xueqian

doi:10.1109/tac.2020.2984723

Cited by 15 publications

(7 citation statements)

References 17 publications

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“…Although the aforementioned difficulty has been alleviated to some extent, the feasible solution still does not always exist, which was pointed out in [2]. Set-membership estimation is another key research direction for switched systems, and zonotopic estimation has become a hot topic recently for its performance in computation and accuracy [10,12,17,21,22]. [10] addressed guaranteed estimation for systems with interval uncertainties by zonotopic approach.…”

Section: Introductionmentioning

confidence: 99%

Zonotopic estimation for switched systems with parameter uncertainty and asynchronous switching

Liu

2023

Preprint

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Variant aircraft is one of the typical applications of switched systems. A zonotopic estimation method for uncertain switched systems with asynchronous switching is proposed in this article because the influence of external disturbance and parameter perturbation widely exists in the flight process of variant aircraft. On the basis of a designed robust observer, the states, errors, disturbances, and uncertain parameters are all described with zonotopes. The ultimate estimation is also derived by utilizing the center vector and generator matrix of zonotope. This method solves the problem of obtaining state information of variant aircraft during flight. Moreover, the interval estimation is verified to be bounded via P-radius definition of zonotope and robust stability theory, and the global optimization of the performance is achieved during the estimation process. Finally, a direct method is used to decrease the computing time and improve the estimation accuracy. The methodology is illustrated to be effective through a simulation of the variant aircraft system.

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Section: Introductionmentioning

confidence: 99%

Zonotopic estimation for switched systems with parameter uncertainty and asynchronous switching

Liu

2023

Preprint

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“…Interval observers in this framework obviously improved estimation accuracy. Additionally, scholars presented a new integrated version of interval observers that achieved an expected tradeoff between robust estimation conservatism and computational complexity [13]. In general, research on interval observers for integer-order systems is fruitful, which is instructive for us to design interval observers of fractional-order systems.…”

Section: Introductionmentioning

confidence: 99%

Fractional-Order Interval Observer for Multiagent Nonlinear Systems

Zhang

Huang

2022

Fractal Fract

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A framework of distributed interval observers is introduced for fractional-order multiagent systems in the presence of nonlinearity. First, a frame was designed to construct the upper and lower bounds of the system state. By using monotone system theory, the positivity of the error dynamics could be ensured, which implies that the bounds could trap the original state. Second, a sufficient condition was applied to guarantee the boundedness of distributed interval observers. Then, an extension of Lyapunov function in the fractional calculus field was the basis of the sufficient condition. An algorithm associated with the procedure of the observer design is also provided. Lastly, a numerical simulation is used to demonstrate the effectiveness of the distributed interval observer.

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“…Besides, zonotope is capable of suppressing the wrapping effect caused by the inflation of estimation sets during each iteration [22]. Recently, zonotope-based approaches have been paid much attention [23]- [26], just mentioned a few. In [23], the advantage of the zonotope approach is elaborately compared with the monotone theory-based means.…”

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confidence: 99%

“…With the help of the UIO form, an extension is carried out in [25] to handle the parameters-varying situation. Moreover, [26] proposes a method by integrating the set theory and positive system theory. It should be noted that most of the above results have not made full use of system outputs to improve the interval estimation accuracy, especially output integrals.…”

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confidence: 99%

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Iterative proportional-integral interval estimation of linear discrete-time systems

Shen

Park

et al. 2022

IEEE Trans. Automat. Contr.

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An iterative proportional-integral interval estimation strategy for linear discrete-time systems is investigated in this paper. A sequence iterative proportional-integral observers are built on system output and unknown disturbance iterative estimation. With the help of a structure separation technique, a sufficient condition in terms of linear matrix inequality is proposed to make the observer error system be asymptotically stable. The boundary reachability of the observer error system is analyzed via zonotope. Zonotope-based iterative algorithms with and without the output integral are built to generate estimated state intervals. Compared with the existing result, the proposed algorithms render tighter estimation intervals illustrated by a simulation study.

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A Novel Set-Theoretic Interval Observer for Discrete Linear Time-Invariant Systems

Cited by 15 publications

References 17 publications

Zonotopic estimation for switched systems with parameter uncertainty and asynchronous switching

Zonotopic estimation for switched systems with parameter uncertainty and asynchronous switching

Fractional-Order Interval Observer for Multiagent Nonlinear Systems

Iterative proportional-integral interval estimation of linear discrete-time systems

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