Sampled-data observers for delay systems and hyperbolic PDE–ODE loops

Ahmed‐Ali, Tarek; Karafyllis, Iasson; Giri, F.

doi:10.1016/j.automatica.2020.109349

Cited by 14 publications

(3 citation statements)

References 38 publications

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“…By means of small‐gain arguments, it is shown there that the equilibrium point

0 \in 𝒞

is GES in the state norm

\mid x(t)\mid +\left\Vert {x}_c\left[t\right]\right\Vert

, provided that

g

is differentiable and the following condition is satisfied:

\underset{x\in \mathbb{R}}{\sup}\kern0.3em {g}^{\prime }(x)<1+\mu {e}^{-\xi /c}.

System (30) was also studied in Reference 28, where a sampled‐data observer was designed with measured output

y(t)={x}_c\left(t,1\right)

and measured input

u(t)

.…”

Section: Application: Chemical Reactor Modelmentioning

confidence: 99%

Building coercive Lyapunov–Krasovskii functionals based on Razumikhin and Halanay approaches

Loko,

Chaillet,

Karafyllis

2024

Intl J Robust & Nonlinear

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In this article, we provide a systematic and constructive way to build a Lyapunov–Krasovskii functional for time‐delay systems whose stability can be established through the Razumikhin or the Halanay approaches. The constructed Lyapunov–Krasovskii functional turns out to be coercive, meaning sandwiched between functions of the state history norm, and to dissipate in terms of the whole history norm. We present these results in the framework of input‐to‐state stability (ISS) in order to further account for the influence of input disturbances. A special emphasis is also given on exponential stability and exponential ISS. We illustrate our findings though the study of a coupled ODE‐PDE model of a chemical reactor, and show that, unlike most results in that area, our approach happens to ensure ISS in terms of the supremum norm of the state.

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“…By means of small‐gain arguments, it is shown there that the equilibrium point

0 \in 𝒞

is GES in the state norm

\mid x(t)\mid +\left\Vert {x}_c\left[t\right]\right\Vert

, provided that

g

is differentiable and the following condition is satisfied:

\underset{x\in \mathbb{R}}{\sup}\kern0.3em {g}^{\prime }(x)<1+\mu {e}^{-\xi /c}.

System (30) was also studied in Reference 28, where a sampled‐data observer was designed with measured output

y(t)={x}_c\left(t,1\right)

and measured input

u(t)

.…”

Section: Application: Chemical Reactor Modelmentioning

confidence: 99%

Building coercive Lyapunov–Krasovskii functionals based on Razumikhin and Halanay approaches

Loko,

Chaillet,

Karafyllis

2024

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

“…It is possible to facilitate the solution of observation and control problems under these conditions by using smart, including adaptive, sensors, in which measurement results are encoded for transmission via a digital communication channel to an appropriately designed decoder. Up to the authors' knowledge, there exist only a few results on robustness with respect to data sampling for parabolic PDE and hyperbolic Partial Differential Equations-Ordinary Differential Equations (PDE-ODE) loops, such as [11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Output Feedback Control of Sine-Gordon Chain over the Limited Capacity Digital Communication Channel

2023

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With the digitalization of mechatronic systems in the conditions of a shortage of available bandwidth of digital communication channels, the problem of ensuring the transfer of information between various components of the system can arise. This problem can be especially challenging in the observation and control of spatially distributed objects due to the complexity of their dynamics, wide frequency band, and other factors. In such cases, a useful approach is to employ smart sensors, in which the measurement results are encoded for transmission over a digital communication channel. Specifically, the article is focused on the transmission of measurement data for the control of energy for a spatially-distributed sine-Gordon chain. The procedures for binary coding of measurements by first- and full-order coder-decoder pairs are proposed and numerically investigated, for each of which the use of stationary and adaptive coding procedures is studied. The procedures for estimating the state of the circuit when measuring outputs are studied, and for each of them, the accuracy of not only estimating the state but also controlling the system by output with the help of an observer is considered. The results of comparative modeling are presented, demonstrating the dependence of the accuracy of estimation and control on the data transfer rate.

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“…This inevitably results in unpredictable performance degradation of the closed‐loop system 11 . To improve the estimation accuracy of observers under complex conditions, the so‐called adaptive observer has attracted much research attention (see References 12 and 13 and the references therein). For example, adaptive extended state observer with automatically tuned gain has been proposed for the discrete‐time system 14,15 .…”

Section: Introductionmentioning

confidence: 99%

Hybrid adaptive extended state observer for event‐triggered networked nonlinear systems subject to deception attacks and external disturbances

Yuan

2022

Intl J Robust & Nonlinear

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In this article, the estimation problem is investigated for a class of continuous-time networked nonlinear systems under both deception attacks and external disturbances. A novel adaptive extended state observer is adopted to estimate the states and disturbance under random deception attacks. The dynamic event-triggered mechanism (ETM) is adopted so as to save the communication resource. Meanwhile, the inter-sample output predictor is proposed to estimate the state between two consecutive triggering instants. The main purpose of the addressed problem is to design the adaptive gain parameters of the novel extended state observer such that the estimation error dynamics is mean-square exponentially bounded stable. Sufficient conditions are first established to ensure the existence of the desired adaptive extended state observer. In addition, it is proven that the Zeno behavior can be avoided when the dynamic ETM is utilized. Finally, a simulation example is provided to verify the effectiveness of the proposed design method.

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Sampled-data observers for delay systems and hyperbolic PDE–ODE loops

Cited by 14 publications

References 38 publications

Building coercive Lyapunov–Krasovskii functionals based on Razumikhin and Halanay approaches

Building coercive Lyapunov–Krasovskii functionals based on Razumikhin and Halanay approaches

Output Feedback Control of Sine-Gordon Chain over the Limited Capacity Digital Communication Channel

Hybrid adaptive extended state observer for event‐triggered networked nonlinear systems subject to deception attacks and external disturbances

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