A survey of model reduction methods for large-scale systems

Antoulas, Athanasios C.; Sorensen, Danny C.; Gugercin, Serkan

doi:10.1090/conm/280/04630

Cited by 550 publications

(443 citation statements)

References 21 publications

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“…Most general purpose model reduction techniques can be classified into either singular value decomposition (SVD) or Krylov-based methods. Research work relating to such concepts can be found in (Antoulas, et al, 2001;Gugercin and Antoulas, 2004;Antoulas, 2005) as a series of recent surveys.…”

Section: Model Reduction Methodsmentioning

confidence: 99%

1-Bit processing based model predictive control for fractionated satellite missions

Bai

2014

Acta Astronautica

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In this thesis, a 1-bit processing based Model Predictive Control (OBMPC) structure is proposed for a fractionated satellite attitude control mission. Despite the appealing advantages of the MPC algorithm towards constrained MIMO control applications, implementing the MPC algorithm onboard a small satellite is certainly challenging due to the limited onboard resources. The proposed design is based on the 1-bit processing concept, which takes advantage of the affine relation between the 1-bit state feedback and multi-bit parameters to implement a multiplier free MPC controller.As multipliers are the major power consumer in online optimization, the OBMPC structure is proven to be more efficient in comparison to the conventional MPC implementation in term of power and circuit complexity. The system is in digital control nature, affected by quantization noise introduced by Δ∑ modulators. The stability issues and practical design criteria are also discussed in this work.Some other aspects are considered in this work to complete the control system. Firstly, the implementation of the OBMPC system relies on the 1-bit state feedbacks. Hence, 1-bit sensing components are needed to implement the OBMPC system. While the ∆∑ modulator based Microelectromechanical systems (MEMS) gyroscope is considered in this work, it is possible to implement this concept into other sensing components.Secondly, as the proposed attitude mission is based on the wireless inter-satellite link (ISL), a state estimator is required. However, conventional state estimators will once again introduce multi-bit signals, and compromise the simple, direct implementation of the OBMPC controller. Therefore, the 1-bit state estimator is also designed in this work to satisfy the requirements of the proposed fractionated attitude control mission.The simulation for the OBMPC is based on a 2U CubeSat model in a fractionated satellite structure, in which the payload and actuators are separated from the controller and controlled via the ISL. Matlab simulations and FPGA implementation based performance analysis shows that the OBMPC is feasible for fractionated satellite missions and is advantageous over the conventional MPC controllers. V VI

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Section: Model Reduction Methodsmentioning

confidence: 99%

1-Bit processing based model predictive control for fractionated satellite missions

Bai

2014

Acta Astronautica

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“…The matrices here do not necessarily have anything to do with the transfer function. Consider 1) where N 1 + N 2 = N . The following theorem describes the structures in a basis matrix of K k (A, B) when one of A ij 's is zero.…”

Section: Structures Of Krylov Subspaces Of Block Matricesmentioning

confidence: 99%

“…Recent survey articles [1,2,7] provide in depth review of the subject and comprehensive references. Roughly speaking, these methods project the original system onto a smaller subspace to arrive at a (much) smaller system having properties, among others, that many leading terms (called moments) of the associated (matrix-valued) transfer functions expanded at given points for the original and reduced systems match.…”

Section: Introductionmentioning

confidence: 99%

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Structure-Preserving Model Reduction

Bai

2006

Applied Parallel Computing. State of the Art in Scientific Computing

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Abstract.A general framework for structure-preserving model reduction by Krylov subspace projection methods is developed. The goal is to preserve any substructures of importance in the matrices L, G, C, B that define the model prescribed by transfer function H(s) = L * (G + sC) −1 B. Many existing structurepreserving model-order reduction methods for linear and second-order dynamical systems can be derived under this general framework.

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“…Unlike many existing model reduction methods such as balanced truncation and Hankel norm approximations [2,39], Krylov projection methods, and in particular the Arnoldi and Lanczos algorithms [4,7,26,27,36], exploit the sparsity of the large scale model and have been extensively used for model reduction of large scale systems; see [3,8,36] and the references therein. In these approaches, G m (s) is computed such that it matches the moments of G(s), that is the value of G(s) and its derivatives, at certain interpolation points.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Rational Interpolation: Arnoldi and Lanczos-like Equations

Frangos

Jaimoukha

2008

European Journal of Control

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The Arnoldi and Lanczos algorithms, which belong to the class of Krylov subspace methods, are increasingly used for model reduction of large scale systems.The standard versions of the algorithms tend to create reduced order models that poorly approximate low frequency dynamics. Rational Arnoldi and Lanczos algorithms produce reduced models that approximate dynamics at various frequencies. This paper tackles the issue of developing simple Arnoldi and Lanczos equations for the rational case. This allows a simple error analysis to be carried out for both algorithms and permits the development of computationally efficient model reduction algorithms, where the frequencies at which the dynamics are to be matched can be updated adaptively.

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A survey of model reduction methods for large-scale systems

Cited by 550 publications

References 21 publications

1-Bit processing based model predictive control for fractionated satellite missions

1-Bit processing based model predictive control for fractionated satellite missions

Structure-Preserving Model Reduction

Adaptive Rational Interpolation: Arnoldi and Lanczos-like Equations

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