Interval observer design and control of uncertain non-homogeneous heat equations

Kharkovskaia, Tatiana; Efimov, Denis; Fridman, Emilia; Polyakov, Andrey; Richard, Jean‐Pierre

doi:10.1016/j.automatica.2019.108595

Cited by 19 publications

(6 citation statements)

References 34 publications

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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%

A Concise Review of State Estimation Techniques for Partial Differential Equation Systems

2021

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While state estimation techniques are routinely applied to systems represented by ordinary differential equation (ODE) models, it remains a challenging task to design an observer for a distributed parameter system described by partial differential equations (PDEs). Indeed, PDE systems present a number of unique challenges related to the space-time dependence of the states, and well-established methods for ODE systems do not translate directly. However, the steady progresses in computational power allows executing increasingly sophisticated algorithms, and the field of state estimation for PDE systems has received revived interest in the last decades, also from a theoretical point of view. This paper provides a concise overview of some of the available methods for the design of state observers, or software sensors, for linear and semilinear PDE systems based on both early and late lumping approaches.

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Section: Robust Synthesismentioning

confidence: 99%

A Concise Review of State Estimation Techniques for Partial Differential Equation Systems

2021

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“…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%

Distributed interval estimation for sensor networks with energy-limited attacks and stochastic communication protocols

Li,

Gong,

Zhu

2024

Transactions of the Institute of Measurement and Control

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In this paper, the problem of the distributed interval estimation is investigated for wireless sensor networks under the energy-limited attack and the stochastic communication protocol (SCP). A model with randomness and restrictions is constructed to describe the energy-limited attack, which is considered to occur in two positions, one is the transmission process of sensors and local estimators (LEs), and another is the transmission process of LEs and their neighbor nodes. Furthermore, to mitigate the communication burden, the SCP is adopted to distribute network access rights to sensor nodes. All in all, the objective of this paper is to develop a distributed interval estimator (DIE) which can use local and neighbor information to generate an interval that covers all potential estimation states when SCP, bounded noises, and energy-limited attacks are all present at the same time. To achieve this, the positive system theory and the stability analysis theory are used to obtain some sufficient conditions for the error dynamic system to be positive system and stable, and the needed DIE gains are achieved by solving the linear matrix inequality. Finally, an example is presented to demonstrate the effectiveness and superiority of the offered method.

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“…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%

Robust Interval Observer for Systems Described by the Fornasini–Marchesini Second Model

Chevet

Rauh

Dinh

et al. 2022

IEEE Control Syst. Lett.

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This letter proposes a novel robust interval observer for a two-dimensional (treated as a synonym for a double-indexed system) linear time-invariant discretetime system described by the Fornasini-Marchesini second model. This system is subject to unknown but bounded state disturbances and measurement noise. Built on recent interval estimation strategies designed for one-dimensional systems, the proposed observer is based on the introduction of weighting matrices which provide additional degrees of freedom in comparison with the classical structure relying on a change of coordinates. Linear matrix inequality conditions for the exponential stability and peak-to-peak performance of a two-dimensional system described by the Fornasini-Marchesini second model are then proposed, and applied to the design of a robust interval observer. Numerical simulation results are provided to show the efficiency of the proposed estimation strategy.

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Interval observer design and control of uncertain non-homogeneous heat equations

Cited by 19 publications

References 34 publications

A Concise Review of State Estimation Techniques for Partial Differential Equation Systems

A Concise Review of State Estimation Techniques for Partial Differential Equation Systems

Distributed interval estimation for sensor networks with energy-limited attacks and stochastic communication protocols

Robust Interval Observer for Systems Described by the Fornasini–Marchesini Second Model

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