Model Reduction for Control System Design

Obinata, Goro; Anderson, Brian D. O.; Lutze, FH

doi:10.1115/1.1399380

Cited by 123 publications

(185 citation statements)

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“…Precisely, under the assumptions given in Theorem II.1 the optimal trajectory z * allows a 47th IEEE CDC, Cancun, Mexico, Dec. [9][10][11]2008 ThB13.2…”

Section: B Port-controlled Hamiltonian Systemsmentioning

confidence: 99%

“…Here, r < 2n is the dimension of the reduced order system. With 47th IEEE CDC, Cancun, Mexico, Dec. [9][10][11]2008 ThB13.2 this decomposition, the system (11) is equivalently described by…”

Section: B Reduced Order Systemsmentioning

confidence: 99%

“…The problem of designing low order controllers for high order or large-scale dynamical systems has received considerable attention in the model reduction community [10]. The most common approach towards solving this problem amounts to first approximating the high order plant by a low order one and subsequently designing a (low order) controller for the low order plant.…”

Section: Introductionmentioning

confidence: 99%

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A Hamiltonian approximation method for the reduction of controlled systems

Weiland

2008

2008 47th IEEE Conference on Decision and Control

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Citation for published version (APA): Weiland, S. (2008). A Hamiltonian approximation method for the reduction of controlled systems. In Proceedings of the 47th IEEE Conference on Decision and Control (CDC 2008) : Mexico, Cancún, 9 -11 December 2008 Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at:openaccess@tue.nl providing details and we will investigate your claim. A Hamiltonian approximation method for the reduction of controlled systems Siep WeilandAbstract-This paper considers the problem of model reduction for controlled systems. The paper considers a dual/adjoint formulation of the general optimization problem to minimize a criterion function subject to plant dynamics and system constraints. By carrying out an approximation on the Lagrangian or Hamiltonian system that is inferred from the dual optimization problem, a reduced Hamiltonian system is obtained that approximates the optimally controlled dynamical system. The merits of the method are illustrated on an example of a controlled binary distillation process.

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“…Precisely, under the assumptions given in Theorem II.1 the optimal trajectory z * allows a 47th IEEE CDC, Cancun, Mexico, Dec. [9][10][11]2008 ThB13.2…”

Section: B Port-controlled Hamiltonian Systemsmentioning

confidence: 99%

Section: B Reduced Order Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Hamiltonian approximation method for the reduction of controlled systems

Weiland

2008

2008 47th IEEE Conference on Decision and Control

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“…Several options exists for this, see, e.g. [6]. Balanced truncation and its generalization was used on a related problem in [9].…”

Section: Lemma 1 Under Assumptions 1-3 It Holdsmentioning

confidence: 99%

“…The techniques we use to solve the problem exploit methods from robust control (model matching [2]) and model reduction (optimal weighted Hankel-norm approximation [3,4,5,6]), and ensure that stable and close-to-optimal subsystems G 1 and G 2 are found. One of the first ideas of using model reduction in system identification is [7].…”

Section: Introductionmentioning

confidence: 99%

Approximative model reconstruction of cascade systems

Hägg

Wahlberg

2014

Systems & Control Letters

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This letter considers how to approximately reconstruct a cascade system from a given unstructured system estimate. Many system identification methods, including subspace methods, provide reliable but generally unstructured black-box models. The problem we consider is how to find cascade systems that are close to such black-box models. For this, we use model matching techniques and optimal weighted Hankel-norm approximation to obtain accurate low-order cascade systems. We show that it is possible to bound the reconstruction error in terms of an error tolerance parameter and weighted Hankel singular values. The suggested methods are illustrated on both a numerical example and a real double tank system with experimental data.

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An ℋ︁_∞algorithm for the windsurfer approach to adaptive robust control

Dehghani

Lanzon

Anderson

2004

Adaptive Control & Signal

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The windsurfing approach to iterative control requires a series of controller designs with the gradual expanding of the closed-loop bandwidth, and in the end in order to stop the algorithm, some validation tests are carried out. In this paper, an H 1 design algorithm is introduced in order to remove the empirical aspect from the stopping criteria and to make the procedure more systematic, hence facilitating the design. Moreover, some restrictive assumptions on the plant model are lifted and some issues with the controller design step are tackled by the introduction of a new design method. This enables us to address a wider class of practical problems.

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Model Reduction for Control System Design

Cited by 123 publications

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A Hamiltonian approximation method for the reduction of controlled systems

A Hamiltonian approximation method for the reduction of controlled systems

Approximative model reconstruction of cascade systems

An ℋ︁_∞algorithm for the windsurfer approach to adaptive robust control

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Model Reduction for Control System Design

Cited by 123 publications

References 0 publications

A Hamiltonian approximation method for the reduction of controlled systems

A Hamiltonian approximation method for the reduction of controlled systems

Approximative model reconstruction of cascade systems

An ℋ︁∞algorithm for the windsurfer approach to adaptive robust control

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An ℋ︁_∞algorithm for the windsurfer approach to adaptive robust control