Balanced realization and model reduction for unstable systems

Zhou, Kemin; Salomon, Gregory; Wu, Eva

doi:10.1002/(sici)1099-1239(199903)9:3<183::aid-rnc399>3.3.co;2-5

Cited by 58 publications

(123 citation statements)

References 3 publications

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“…These balanced modes have been introduced more than two decades ago (Moore 1981) and have been applied to small and moderately sized problems; even extensions to unstable systems (Zhou, Salomon & Wu 1999) and nonlinear control problems (Scherpen 1993;Lall, Marsden & Glavaski 2002) have been developed. the ability of the applied forcing to reach flow states, and observability, i.e.…”

Section: Introductionmentioning

confidence: 99%

Closed-loop control of an open cavity flow using reduced-order models

Sipp²,

2009

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International audienceThe control of separated fluid flow by reduced-order models is studied using the two-dimensional incompressible flow over an open square cavity at Reynolds numbers where instabilities are present. Actuation and measurement locations are taken on the upstream and downstream edge of the cavity. A bi-orthogonal projection is introduced to arrive at reduced-order models for the compensated problem. Global modes, proper orthogonal decomposition (POD) modes and balanced modes are used as expansion bases for the model reduction. The open-loop behaviour of the full and the reduced systems is analysed by comparing the respective transfer functions. This analysis shows that global modes are inadequate to sufficiently represent the inputoutput behaviour whereas POD and balanced modes are capable of properly approximating the exact transfer function. Balanced modes are far more efficient in this process, but POD modes show superior robustness. The performance of the closed-loop system corroborates this finding: while reduced-order models based on POD are able to render the compensated system stable, balanced modes accomplish the same with far fewer degrees of freedom. © 2009 Cambridge University Press

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Section: Introductionmentioning

confidence: 99%

Closed-loop control of an open cavity flow using reduced-order models

Sipp²,

2009

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“…The central result of this paper is that techniques developped for solving the Lyapunov equations [13][14][15] enable us to define the neighborhood of a hyperbolic periodic point by splitting the covariance matrix Q into two (mutually non-orthogonal) covariance matrices, Q cc for contracting directions, and Q ee for the expanding directions.…”

Section: A Width Of a Noisy Trajectorymentioning

confidence: 99%

Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system

2015

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The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the stochastic neighborhoods of deterministic periodic orbits can be computed from distributions stationary under the action of a local FokkerPlanck operator and its adjoint. We derive explicit formulae for widths of these distributions in the case of chaotic dynamics, when the periodic orbits are hyperbolic. The resulting neighborhoods form a basis for functions on the attractor. The global stationary distribution, needed for calculation of long-time expectation values of observables, can be expressed in this basis.

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“…For an application of model reduction based on balanced truncation to unstable and non-minimal systems, see [33,34,35].…”

Section: Remark 2 Note That the Mjls Is Minimal If And Only If It Ismentioning

confidence: 99%

Balanced truncation approach to model reduction of Markovian jump time-varying delay systems

Zhang

Shi

et al. 2015

Journal of the Franklin Institute

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Balanced realization and model reduction for unstable systems

Cited by 58 publications

References 3 publications

Closed-loop control of an open cavity flow using reduced-order models

Closed-loop control of an open cavity flow using reduced-order models

Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system

Balanced truncation approach to model reduction of Markovian jump time-varying delay systems

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