Empirical model reduction of controlled nonlinear systems

Lall, Sanjay; Marsden, Jerrold E.; Glavaski, S.

doi:10.1016/s1474-6670(17)56442-3

Cited by 146 publications

(154 citation statements)

References 8 publications

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“…It is the method of empirical grammians. Its goal is to remedy the issues arising in POD methods, at the expense of added computational complexity [52]. A different set of approximation methods have been developed.…”

Section: Approximation Methodsmentioning

confidence: 99%

Approximation of Large-Scale Dynamical Systems: An Overview

Antoulas

2004

IFAC Proceedings Volumes

143

178

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In this paper we review the state of affairs in the area of approximation of large-scale systems. We distinguish among three basic categories, namely the SVD-based, the Krylov-based and the SVD-Krylov-based approximation methods. The first two were developed independently of each other and have distinct sets of attributes and drawbacks. The third approach seeks to combine the best attributes of the first two.

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Section: Approximation Methodsmentioning

confidence: 99%

Approximation of Large-Scale Dynamical Systems: An Overview

Antoulas

2004

IFAC Proceedings Volumes

143

178

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“…The relationship between balancing and the KLE method was developed in the papers by Lall et al [17,18], where a method of using the KLE in order to construct the balanced truncation of a linear system of n first-order differential equations was constructed. In fact, the standard KLE methods applied to linear systems in first-order form is equivalent to the method known as input-balancing for controlled systems with a single-input.…”

Section: Previous Workmentioning

confidence: 99%

Structure-preserving model reduction for mechanical systems

Lall¹,

Krysl²,

Marsden³

2003

Physica D: Nonlinear Phenomena

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138

112

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This paper focuses on methods of constructing of reduced-order models of mechanical systems which preserve the Lagrangian structure of the original system. These methods may be used in combination with standard spatial decomposition methods, such as the Karhunen-Loève expansion, balancing, and wavelet decompositions. The model reduction procedure is implemented for three-dimensional finite-element models of elasticity, and we show that using the standard Newmark implicit integrator, significant savings are obtained in the computational costs of simulation. In particular simulation of the reduced model scales linearly in the number of degrees of freedom, and parallelizes well.

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“…Thus observable modes, structures with quantified observability given by the corresponding eigenvalue, are represented. A generalized balanced truncation of nonlinear systems has been proposed by Lall, Marsden & Glavaški (1999 using generalized empirical Gramians. The generalization of empirical observability Gramians enables the definition of the observable modes to be the eigenfunction of a generalized empirical observability Gramian.…”

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confidence: 99%

On least-order flow representations for aerodynamics and aeroacoustics

et al. 2012

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We propose a generalization of proper orthogonal decomposition (POD) for optimal flow resolution of linearly related observables. This Galerkin expansion, termed 'observable inferred decomposition' (OID), addresses a need in aerodynamic and aeroacoustic applications by identifying the modes contributing most to these observables. Thus, OID constitutes a building block for physical understanding, leastbiased conditional sampling, state estimation and control design. From a continuum of OID versions, two variants are tailored for purposes of observer and control design, respectively. Firstly, the most probable flow state consistent with the observable is constructed by a 'least-residual' variant. This version constitutes a simple, easily generalizable reconstruction of the most probable hydrodynamic state to preprocess efficient observer design. Secondly, the 'least-energetic' variant identifies modes with the largest gain for the observable. This version is a building block for Lyapunov control design. The efficient dimension reduction of OID as compared to POD is demonstrated for several shear flows. In particular, three aerodynamic and aeroacoustic goal functionals are studied: (i) lift and drag fluctuation of a two-dimensional cylinder wake flow; (ii) aeroacoustic density fluctuations measured by a sensor array and emitted from a two-dimensional compressible mixing layer; † Email address for correspondence: michael.schlegel@tu-berlin.de

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Empirical model reduction of controlled nonlinear systems

Cited by 146 publications

References 8 publications

Approximation of Large-Scale Dynamical Systems: An Overview

Approximation of Large-Scale Dynamical Systems: An Overview

Structure-preserving model reduction for mechanical systems

On least-order flow representations for aerodynamics and aeroacoustics

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