Efficient Modeling and Control of Large-Scale Systems

Mohammadpour, Javad; Grigoriadis, Karolos

doi:10.1007/978-1-4419-5757-3

Cited by 37 publications

(12 citation statements)

References 17 publications

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“…Assuming possibly coinciding source-receiver pairs, we can define the source/receiver array as B s = [b [1] , . .…”

Section: Formulation Of a Block Methodmentioning

confidence: 99%

“…We start by approximating the weak solution of equation (2.7) by an element from the space K 2m R (κ). To this end, let the functions v [1] , v [2] , ...,v [2m] form a real basis V m ∈ R ∞×2m of K 2m R (κ). The reduced-order solution is now expanded as u m = V m z with expansion coefficients α i collected in vector z = [α 1 , ..., α 2m ] T .…”

Section: Reduced-order Solutionmentioning

confidence: 99%

“…The standard theory of Galerkin interpolatory-projection model reduction of passive, self-adjoint, dynamic systems yields the following interpolation properties (e.g., see [1]). which has double zeros at s = κ ∪ κ, since the error and residual vanishes for these frequencies due to relation (3.6).…”

Section: Interpolation Propertiesmentioning

confidence: 99%

“…we can construct reduced-order models in the usual way, but now in terms of frequency-dependent basis functions. More precisely, let M ≤ 4m be the dimension of K 4m EIK;R (κ, s) and let vectors v [1]…”

Section: Field Parametrization For Siso Problemsmentioning

confidence: 99%

“…The time-domain multiscale algorithms can be efficiently parallelized via domain-decomposition, but time stepping still needs to be carried out sequentially, while frequency-domain problems can be solved in parallel for different frequencies. Here we consider interpolatory projection-based model reduction in the frequency-domain, e.g., see [1]. The essence of this approach is the projection of the underlying system onto a rational Krylov subspace (originally introduced by Ruhe for eigenvalue computations [24]), which produces good quality, low order approximations if the spectrum of the system is well separated from the frequency interval of interest, as in the case of diffusion PDEs, e.g., [2,13,20,16].…”

mentioning

confidence: 99%

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Compressing Large-Scale Wave Propagation Models via Phase-Preconditioned Rational Krylov Subspaces

Druskin¹,

Remis²,

Zaslavsky³

et al. 2018

Multiscale Model. Simul.

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Rational Krylov subspace (RKS) techniques are well-established and powerful tools for projection-based model reduction of time-invariant dynamic systems. For hyperbolic wavefield problems, such techniques perform well in configurations where only a few modes contribute to the field. RKS methods, however, are fundamentally limited by the Nyquist-Shannon sampling rate, making them unsuitable for the approximation of wavefields in configuration characterized by large travel times and propagation distances, since wavefield responses in such configurations are highly oscillatory in the frequency-domain. To overcome this limitation, we propose to precondition the RKSs by factoring out the rapidly varying frequency-domain field oscillations. The remaining amplitude functions are generally slowly varying functions of source position and spatial coordinate and allow for a significant compression of the approximation subspace. Our one-dimensional analysis together with numerical experiments for large scale 2D acoustic models show superior approximation properties of preconditioned RKS compared with the standard RKS model-order reduction. The preconditioned RKS results in a reduction of the frequency sampling well below the Nyquist-Shannon rate, a weak dependence of the RKS size on the number of inputs and outputs for multiple-input/multiple-output (MIMO) problems, and, most importantly, in a significant coarsening of the finite-difference grid used to generate the RKS. A prototype implementation indicates that the preconditioned RKS algorithm is competitive in the modern high performance computing environment.AMS subject classifications. 65M60, 65M80, 93B11, 37M05, 78A05 1. Introduction. Numerical modeling of wave propagation is fundamental to many applications in design optimization and wavefield imaging. In the oil and gas industry, for instance, the solution of the Maxwell equations is required to invert electromagnetic measurements, while in seismic imaging the solution to the elastodynamic wave equation is needed to ultimately image the subsurface of the Earth.Finite difference discretization of the governing wave equations leads to large-scale linear systems, whose solution is computationally intense. Imaging and optimization often use multiple frequencies, sources, and receivers, which leads to systems that need to be evaluated for multiple right-hand sides, time-steps or frequencies, depending on whether the problem is solved in the time-or frequency-domain. Therefore, these so-called multiple-input/multiple-output (MIMO) systems have a high demand on memory and computational power, causing long runtimes. To be more specific, let us consider a surface seismic imaging problem in a k dimensional space (1 ≤ k ≤ 3), with maximal propagation distance of N wavelengths. This would require the solution of a discretized system with O(N k ) state variables, O(N k−1 ) sources and receivers, and O(N ) frequencies or time steps [22]. Model-order reduction aims to reduce the complexity and computational burden of large-scale pro...

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“…Assuming possibly coinciding source-receiver pairs, we can define the source/receiver array as B s = [b [1] , . .…”

Section: Formulation Of a Block Methodmentioning

confidence: 99%

Section: Reduced-order Solutionmentioning

confidence: 99%

Section: Interpolation Propertiesmentioning

confidence: 99%

Section: Field Parametrization For Siso Problemsmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Compressing Large-Scale Wave Propagation Models via Phase-Preconditioned Rational Krylov Subspaces

Druskin¹,

Remis²,

Zaslavsky³

et al. 2018

Multiscale Model. Simul.

View full text Add to dashboard Cite

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Decentralized adaptive terminal sliding mode control design for nonlinear connected system in the presence of external disturbance

RanjbarBabak

NoieyAbolfazl

Rezaie

2021

Adaptive Control & Signal

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In this article, a decentralized adaptive integral terminal sliding mode control is presented for a class of nonlinear connected systems. It is assumed that the system is also confronted by unknown disturbances, while the interconnections between subsystems are assumed unknown. An integral terminal sliding surface for each subsystem is locally considered to guarantee the stability of the closed-loop system, and to increase the convergence speed during a tracking task. The unknown interconnections between subsystems are estimated using adaptive rules. An appropriate Lyapunov candidate is chosen to perform global stability analysis. In this regard, design parameters are chosen such that the closed-loop stability is ensured. Performance of the proposed method for a mechanical connected system, including two chaotic subsystems, is shown through simulations.

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Finite‐time boundedness of large‐scale systems with actuator faults and gain fluctuations

Tharanidharan

Sakthivel

Kaviarasan

et al. 2019

Intl J Robust & Nonlinear

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Summary This paper addresses the issue of finite‐time boundedness of large‐scale interconnected systems with the use of a distributed nonfragile fault‐tolerant controller. The objective of this paper is to design a state‐feedback controller consisting of a time‐varying delay such that the resulting closed‐loop system is finite‐time bounded under a prescribed extended passivity performance level even in the presence of all admissible uncertainties and possible actuator faults. More precisely, based on the Lyapunov‐Krasovskii stability theory, a new set of sufficient conditions is obtained in the framework of linear matrix inequality constraints that ensures finite‐time boundedness and satisfies the prescribed extended passivity performance index of the considered system. Finally, two numerical examples, including the interconnected inverted pendulum, are given to show the effectiveness of the proposed controller design technique.

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Efficient Modeling and Control of Large-Scale Systems

Cited by 37 publications

References 17 publications

Compressing Large-Scale Wave Propagation Models via Phase-Preconditioned Rational Krylov Subspaces

Compressing Large-Scale Wave Propagation Models via Phase-Preconditioned Rational Krylov Subspaces

Decentralized adaptive terminal sliding mode control design for nonlinear connected system in the presence of external disturbance

Finite‐time boundedness of large‐scale systems with actuator faults and gain fluctuations

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