Sensitivity Shaping With Degree Constraint by Nonlinear Least-Squares Optimization

Nagamune, Ryozo; Blomqvist, A.

doi:10.3182/20050703-6-cz-1902.01028

Cited by 11 publications

(13 citation statements)

References 9 publications

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“…The solutions are obtained as minimizers of suitable weighted entropy functionals. We build on recent insights by Nagamune, Blomqvist, and others (see, e.g., [2]- [5], [17]), and we focus on how to efficiently shape closed-loop transfer functions via suitable choices of the relevant weights. In turn, the weights themselves are obtained by solving another optimization problem which takes into account performance specifications.…”

Section: Discussionmentioning

confidence: 99%

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Weight Selection in Interpolation with a Dimensionality Constraint

Takyar

Amini

Georgiou

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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The topic of the paper relates to a recent parametrization of analytic interpolants with a bound on their dimension, as solutions to certain weighted entropy minimization problems. The analytic interpolation problem arises in the context of shaping closed-loop transfer functions via a suitable choice of controller. Our goal is to shed light on how the choice of weights affects the shape of the corresponding closed-loop transfer functions. Further, given a desirable shape, we indicate how a suitable weight can be obtained as a solution of a certain quasi-convex problem.

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Section: Discussionmentioning

confidence: 99%

“…Using the corresponding Φ d and running (9) provides a Ψ with zeros at 0.6986±0.6015i and 0. (16) and (17).…”

Section: Examplesmentioning

confidence: 99%

Weight Selection in Interpolation with a Dimensionality Constraint

Takyar

Amini

Georgiou

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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“…However, Antoulas' observation does not come as great surprise to us, since the concept of spectral zeros is a key ingredient in a theory of analytic interpolation developed over the last decades by Byrnes, Georgiou, Lindquist and their coworkers [3]- [12], [14]- [21], [23], [24], [26]. Indeed, given k + 1 interpolation points and corresponding interpolation values, the class of all analytic interpolants of McMillan degree at most k is completely parameterized by the stable spectral zeros.…”

Section: Introductionmentioning

confidence: 94%

A Global Analysis Approach to Passivity Preserving Model Reduction

Fanizza¹,

Karlsson²,

Lindquist³

et al. 2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Passivity-preserving model reduction for linear time-invariant systems amounts to approximating a positivereal rational transfer function with one of lower degree. Recently Antoulas and Sorensen have proposed such a modelreduction method based on Krylov projections. The method is based on an observation by Antoulas (in the single-input/singleoutput case) that if the approximant is preserving a subset of the spectral zeros and takes the same values as the original transfer function in the mirror points of the preserved spectral zeros, then the approximant is also positive real. However, this turns out to be a special solution in the theory of analytic interpolation with degree constraint developed by Byrnes, Georgiou and Lindquist, namely the maximum-entropy (central) solution. By tuning the interpolation points and the spectral zeros, as prescribed by this theory, one is able to obtain considerably better reduced-order models.

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“…These roots coincide with the spectral zeros of the corresponding minimizers of the weighted entropy functionals [12]. The choice of weights for feedback control design via this procedure has been the subject of several papers (see, e.g., [34], [35]). The challenge stems from the fact that the correspondence between weights and the shape of interpolants is nonlinear.…”

Section: Introductionmentioning

confidence: 98%

The Inverse Problem of Analytic Interpolation With Degree Constraint and Weight Selection for Control Synthesis

Karlsson

Georgiou

Lindquist

2010

IEEE Trans. Automat. Contr.

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The minimizers of certain weighted entropy functionals are the solutions to an analytic interpolation problem with a degree constraint, and all solutions to this interpolation problem arise in this way by a suitable choice of weights. Selecting appropriate weights is pertinent to feedback control synthesis, where interpolants represent closed-loop transfer functions. In this paper we consider the correspondence between weights and interpolants in order to systematize feedback control synthesis with a constraint on the degree. There are two basic issues that we address: we first characterize admissible shapes of minimizers by studying the corresponding inverse problem, and then we develop effective ways of shaping minimizers via suitable choices of weights. This leads to a new procedure for feedback control synthesis.

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Sensitivity Shaping With Degree Constraint by Nonlinear Least-Squares Optimization

Cited by 11 publications

References 9 publications

Weight Selection in Interpolation with a Dimensionality Constraint

Weight Selection in Interpolation with a Dimensionality Constraint

A Global Analysis Approach to Passivity Preserving Model Reduction

The Inverse Problem of Analytic Interpolation With Degree Constraint and Weight Selection for Control Synthesis

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