2020
DOI: 10.1016/j.automatica.2019.108595
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Interval observer design and control of uncertain non-homogeneous heat equations

Abstract: The problems of state estimation and observer-based control for heat non-homogeneous equations under distributed in space point measurements are considered. First, an interval observer is designed in the form of Partial Differential Equations (PDEs), without Galerkin projection. Second, conditions of boundedness of the interval observer solutions with non-zero boundary conditions and measurement noise are proposed. Third, the obtained interval estimates are used to design a dynamic outputfeedback stabilizing c… Show more

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Cited by 20 publications
(6 citation statements)
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“…The interval width is linked to the size of the model uncertainty. There are several approaches to design interval/set-membership estimators for PDE systems within which we can cite [83][84][85].…”
Section: Robust Synthesismentioning
confidence: 99%
“…The interval width is linked to the size of the model uncertainty. There are several approaches to design interval/set-membership estimators for PDE systems within which we can cite [83][84][85].…”
Section: Robust Synthesismentioning
confidence: 99%
“…Motivated by the above discussion, the main objective of this paper is to design a DIE for sensor networks with SCP and the energy-limited assault. The main idea of the DIE is to design the estimator gain matrix using the information of sensor nodes and their neighbor nodes such that the actual state is contained within an estimation interval (Gu et al, 2023; Huang et al, 2020; Kharkovskaia et al, 2020; Li et al, 2020a; Xu et al, 2020). The following are some of the article’s unique characteristics: (a) A DIE is developed for wireless sensor networks that can provide real-time upper and lower bounds of the system state in the presence of energy-limited DoS attacks and bounded noises, which improves the adaptability of the DIE.…”
Section: Introductionmentioning
confidence: 99%
“…To the authors' knowledge, interval observers for partial differential equations have been investigated [26], [27], but no interval observers for 2D systems have been proposed. Therefore, this letter proposes to build a robust interval observer for a 2D discrete-time linear time-invariant (LTI) system described by the Fornasini-Marchesini second (FM-II) model (defined in Section II.B).…”
Section: Introductionmentioning
confidence: 99%