On convergence conditions of waveform relaxation methods for linear differential-algebraic equations

Bai, Zhong‐Zhi; Yang, Xi

doi:10.1016/j.cam.2010.11.031

Cited by 15 publications

(15 citation statements)

References 8 publications

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“…To overcome this continuous communication obstacle we rely on waveform relaxation methods [44], [45] developed for parallel numerical integration. The Gauss-Jacobi waveform relaxation applied to the filter (10) yields the waveform relaxation iteration…”

Section: Proofmentioning

confidence: 99%

Attack Detection and Identification in Cyber-Physical Systems

Pasqualetti

Dörfler

Bullo

2013

IEEE Trans. Automat. Contr.

1,829

1,166

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Cyber-physical systems are ubiquitous in power systems, transportation networks, industrial process control and critical infrastructures. These systems need to operate reliably in the face of unforeseen failures and external malicious attacks. In this paper (i) we propose a mathematical framework for cyberphysical systems, attacks, and monitors; (ii) we characterize fundamental monitoring limitations from system-theoretic and graph-theoretic perspectives; and (iii) we design centralized and distributed attack detection and identification monitors. Finally, we validate our findings through compelling examples.

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Section: Proofmentioning

confidence: 99%

Attack Detection and Identification in Cyber-Physical Systems

Pasqualetti

Dörfler

Bullo

2013

IEEE Trans. Automat. Contr.

1,829

1,166

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“…An elegant analysis of the waveform relaxation iteration (10) can be carried out in the Laplace domain [23], where the map from…”

Section: B Decentralized Estimation and Waveform Relaxationmentioning

confidence: 99%

“…Our continuous-discrete algorithm is inspired by our earlier investigation of waveform relaxation methods [17]- [19], and it combines decentralized control techniques [6], [20] with waveform relaxation methods developed for parallel numerical integration [21]- [23]. Compared to our earlier work and the waveform relaxation literature, our current approach is based on state-space analysis.…”

Section: Introductionmentioning

confidence: 99%

“…Compared to our earlier work and the waveform relaxation literature, our current approach is based on state-space analysis. Thanks to this novel approach, we can derive a necessary and sufficient convergence condition reminiscent of the small-gain and spectral radius criteria found in the literature on decentralized estimation [6], [20] and waveform relaxation [21]- [23]. We further derive convergence rate estimates as well as sufficient conditions for contractivity of the estimation error for a finite number of communication rounds and measurements collected in a finite-time horizon.…”

Section: Introductionmentioning

confidence: 99%

“…This continuous communication obstacle can be overcome by means of a parallel integration of the filter (6). Among the available methods developed for parallel computation, the classical waveform relaxation is compatible with assumptions (A1)-(A4) [21]- [23]. The GaussJacobi waveform relaxation method applied to the filter (6) yields the waveform relaxation iteratioṅ…”

Section: B Decentralized Estimation and Waveform Relaxationmentioning

confidence: 99%

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Continuous-Time Distributed Observers With Discrete Communication

Dörfler

Pasqualetti

Bullo

2013

IEEE J. Sel. Top. Signal Process.

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Abstract-This work presents a distributed algorithm for observer design for linear continuous-time systems. We assume the dynamical system to be partitioned into disjoint areas, and we let each area be equipped with a control center. Each control center knows local dynamics, collects local observations, performs local computation, and communicates with neighboring control centers at discrete times. For our continuous-discrete estimation algorithm we prove convergence, we characterize its convergence rate, and we show robustness against discretization and communication errors. Our technical approach is inspired by waveform relaxation methods and combines tools from estimation theory, decentralized control theory, and parallel computation. We illustrate the effectiveness of our algorithm with illustrative examples in sensor networks and electric power systems.

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Modular‐Based Simulation of Single Process Units

Dosta

2019

Chem Eng & Technol

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A novel simulation strategy for the modular-based calculation of models describing single unit operations is proposed. It is based on the functional decomposition of the model with further application of the waveform relaxation approach for data exchange and convergence analysis. Compared to convenient simultaneous calculation of units, the proposed approach leads to higher flexibility during model creation and allow simultaneous usage of several solvers and simulation methods. To illustrate the usability of the developed strategy and analyze its efficiency it has been applied for modeling of a fluidized-bed spray granulator. Based on the functional decomposition, the granulator model has been decomposed into six separate submodels connected with information streams for data exchange.

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On convergence conditions of waveform relaxation methods for linear differential-algebraic equations

Cited by 15 publications

References 8 publications

Attack Detection and Identification in Cyber-Physical Systems

Attack Detection and Identification in Cyber-Physical Systems

Continuous-Time Distributed Observers With Discrete Communication

Modular‐Based Simulation of Single Process Units

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