Model reduction of large-scale interconnected systems

Feliachi, A.; Bhurtun, C.

doi:10.1080/00207728708967185

Cited by 11 publications

(5 citation statements)

References 7 publications

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“…Reducibility and an H2 Error Bound. The pioneering work on clustering-based model reduction of dynamic networks in (24,49) introduces a notion of cluster reducibility, which is relevant to the classic notions exact aggregation and approximate aggregation from the control and model reduction literature (75,76).…”

Section: Clustering Meets Optimizationmentioning

confidence: 99%

Model Reduction Methods for Complex Network Systems

Cheng

Scherpen

2021

Annu. Rev. Control Robot. Auton. Syst.

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Network systems consist of subsystems and their interconnections and provide a powerful framework for the analysis, modeling, and control of complex systems. However, subsystems may have high-dimensional dynamics and a large number of complex interconnections, and it is therefore relevant to study reduction methods for network systems. Here, we provide an overview of reduction methods for both the topological (interconnection) structure of a network and the dynamics of the nodes while preserving structural properties of the network. We first review topological complexity reduction methods based on graph clustering and aggregation, producing a reduced-order network model. Next, we consider reduction of the nodal dynamics using extensions of classical methods while preserving the stability and synchronization properties. Finally, we present a structure-preserving generalized balancing method for simultaneously simplifying the topological structure and the order of the nodal dynamics. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 4 is May 3, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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Section: Clustering Meets Optimizationmentioning

confidence: 99%

Model Reduction Methods for Complex Network Systems

Cheng

Scherpen

2021

Annu. Rev. Control Robot. Auton. Syst.

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“…The initial condition of (6) is x(0) = x 10 T ⋯ x k0 T T . The system (6) is called the closed-loop system of the coupled system (1)- (3).…”

Section: ε-Embedding Technique Of the Closed-loop Systemmentioning

confidence: 99%

“…Then, the subsystems (23) and (24) coupled through the interconnected relations (2) and (3) can be regarded as an approximation of the coupled system (1)- (3). The transfer function of the approximate coupled system can be written as…”

Section: ε-Embedding Technique Of Subsystemsmentioning

confidence: 99%

“…The development of technology and industry has aroused great interest in the study of coupled systems, which emerge in many fields, such as elastic multibody systems, very large system integrated (VLSI) chip designs, and micro‐electro‐mechanical systems [1, 2]. Model order reduction (MOR) of coupled systems has been studied in the 1980s [3]. Its goal is to replace the original large‐scale system by a small one such that the computation cost is significantly reduced and the efficiency of the simulation is obviously improved.…”

Section: Introductionmentioning

confidence: 99%

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Balanced truncation with ε‐embedding for coupled dynamical systems

Jiang

Chen

Yang

2018

IET Circuits, Devices & Systems

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The authors focus on exploring the ε-embedding balanced truncation method of coupled systems. First, the coupled system is converted into a closed-loop system. Then, the ε-embedding technique and the Cholesky factor-alternating direction implicit algorithm are introduced to establish the balanced truncation method. The error bound and the stability of the resulting reduced-order system are discussed. Furthermore, the proposed method is applied to reduce the order of each subsystem such that the original interconnected structure is preserved. The error bound and the stability of the corresponding reduced-order system are also investigated. Finally, two numerical examples are employed to demonstrate the efficiency of the proposed method.

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“…MOR for coupled systems was originally discussed in [15] and in the past years, several achievements on such topic have been achieved. Generally speaking, there are two kinds of MOR approaches for coupled systems.…”

Section: Introductionmentioning

confidence: 99%

Structure‐preserved MOR method for coupled systems via orthogonal polynomials and Arnoldi algorithm

Jiang

Xiao

2019

IET Circuits, Devices & Systems

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This study focuses on the topic of model order reduction (MOR) for coupled systems with inhomogeneous initial conditions and presents an MOR method by general orthogonal polynomials with Arnoldi algorithm. The main procedure is to use a series of expansion coefficients vectors in the space spanned by orthogonal polynomials that satisfy a recursive formula to generate a projection based on the multiorder Arnoldi algorithm. The resulting model not only match desired number of expansion coefficients but also has the same coupled structure as the original system. Moreover, the stability is preserved as well. The error bound between the outputs is well-discussed. Finally, numerical results show that the authors' method can deal well with those systems with inhomogeneous initial conditions in the views of accuracy and computational cost.

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Model reduction of large-scale interconnected systems

Cited by 11 publications

References 7 publications

Model Reduction Methods for Complex Network Systems

Model Reduction Methods for Complex Network Systems

Balanced truncation with ε‐embedding for coupled dynamical systems

Structure‐preserved MOR method for coupled systems via orthogonal polynomials and Arnoldi algorithm

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