Bilinear PMOR method - Revision history

Breiten at 05:59, 30 May 2013

2013-05-30T05:59:51Z

← Older revision		Revision as of 05:59, 30 May 2013
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	For a detailed analysis of this approach, we refer to e.g. <ref>P. Benner and T. Damm, "<span class="plainlinks">[http://dx.doi.org/10.1137/09075041X Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems]</span>", SIAM J. Cont. Optim., 49 (2011), pp. 686-711.</ref>. Another possibility is to aim at a model reduction method which is optimal with respect to a certain system norm. In <ref>P. Benner and T. Breiten, "<span class="plainlinks">[http://www.mpi-magdeburg.mpg.de/preprints/2011/MPIMD11-02.pdf Interpolation-based H2-model reduction of bilinear control systems]</span>", 2011, Preprint MPIMD/11-02.</ref>, the authors investigate a possible extension of the linear <math>H_2</math>-norm and propose an algorithm which extends the well-known iterative rational Krylov algorithm (IRKA) to the bilinear setting specified above.		For a detailed analysis of this approach, we refer to e.g. <ref>P. Benner and T. Damm, "<span class="plainlinks">[http://dx.doi.org/10.1137/09075041X Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems]</span>", SIAM J. Cont. Optim., 49 (2011), pp. 686-711.</ref>. Another possibility is to aim at a model reduction method which is optimal with respect to a certain system norm. In <ref>P. Benner and T. Breiten, "<span class="plainlinks">[http://www.mpi-magdeburg.mpg.de/preprints/2011/MPIMD11-02.pdf Interpolation-based H2-model reduction of bilinear control systems]</span>", 2011, Preprint MPIMD/11-02.</ref>, the authors investigate a possible extension of the linear <math>H_2</math>-norm and propose an algorithm which extends the well-known iterative rational Krylov algorithm ([[IRKA\|IRKA]]) to the bilinear setting specified above.

	Both methods have been tested on several LPV control systems (e.g., [[Microthruster_Unit\|Microthruster Unit]] and [[Scanning_Electrochemical_Microscopy\|Scanning Electrochemical Microscopy]]) and seem to be a reasonable alternative to existing parametric model reduction methods.		Both methods have been tested on several LPV control systems (e.g., [[Microthruster_Unit\|Microthruster Unit]] and [[Scanning_Electrochemical_Microscopy\|Scanning Electrochemical Microscopy]]) and seem to be a reasonable alternative to existing parametric model reduction methods.

Himpe: references with cite, reference link

2013-04-24T11:47:44Z

references with cite, reference link

← Older revision		Revision as of 11:47, 24 April 2013
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	As one can see, there seems to be a close connection between LPV and bilinear systems which may be advantageous. To be more precise, following [2], we can interpret LPV systems as special bilinear system by simply setting		As one can see, there seems to be a close connection between LPV and bilinear systems which may be advantageous. To be more precise, following <ref>P. Benner and T. Breiten, "<span class="plainlinks">[http://dx.doi.org/10.1002/pamm.201110391 On H2-model reduction of linear parameter-varying systems]</span>", In Proceedings in Applied Mathematics and Mechanics. Wiley InterScience, 2011.</ref>, we can interpret LPV systems as special bilinear system by simply setting

	<math>		<math>
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	For a detailed analysis of this approach, we refer to e.g. [3]. Another possibility is to aim at a model reduction method which is optimal with respect to a certain system norm. In [1], the authors investigate a possible extension of the linear <math>H_2</math>-norm and propose an algorithm which extends the well-known iterative rational Krylov algorithm (IRKA) to the bilinear setting specified above.		For a detailed analysis of this approach, we refer to e.g. <ref>P. Benner and T. Damm, "<span class="plainlinks">[http://dx.doi.org/10.1137/09075041X Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems]</span>", SIAM J. Cont. Optim., 49 (2011), pp. 686-711.</ref>. Another possibility is to aim at a model reduction method which is optimal with respect to a certain system norm. In <ref>P. Benner and T. Breiten, "<span class="plainlinks">[http://www.mpi-magdeburg.mpg.de/preprints/2011/MPIMD11-02.pdf Interpolation-based H2-model reduction of bilinear control systems]</span>", 2011, Preprint MPIMD/11-02.</ref>, the authors investigate a possible extension of the linear <math>H_2</math>-norm and propose an algorithm which extends the well-known iterative rational Krylov algorithm (IRKA) to the bilinear setting specified above.

	Both methods have been tested on several LPV control systems (e.g., [[Microthruster_Unit\|Microthruster Unit]] and [[Scanning_Electrochemical_Microscopy\|Scanning Electrochemical Microscopy]]) and seem to be a reasonable alternative to existing parametric model reduction methods.		Both methods have been tested on several LPV control systems (e.g., [[Microthruster_Unit\|Microthruster Unit]] and [[Scanning_Electrochemical_Microscopy\|Scanning Electrochemical Microscopy]]) and seem to be a reasonable alternative to existing parametric model reduction methods.
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	==References==		==References==

	~~[1] P. Benner and T. Breiten, Interpolation-based H2-model reduction of bilinear control systems, 2011, Preprint MPIMD~~/~~11-02.~~		<references/>

	~~[2] P. Benner and T. Breiten, On H2-model reduction of linear parameter-varying~~
	~~systems, In Proceedings in Applied Mathematics and Mechanics. Wiley InterScience,~~
	~~2011.~~

	~~[3] P. Benner and T. Damm, Lyapunov Equations, Energy Functionals, and Model Order Reduction~~
	~~of Bilinear and Stochastic Systems, SIAM J. Cont. Optim., 49 (2011), pp. 686-711.~~

	==Contact==		==Contact==

	'' [[User:breiten\|Tobias Breiten]]''		'' [[User:breiten\|Tobias Breiten]]''

Baur: changes of categories

2013-04-19T21:10:12Z

changes of categories

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	[[Category:method]]		[[Category:method]]
	[[Category:~~non-linear method~~]]		[[Category:nonlinear]]
	[[Category:parametric ~~method~~]]		[[Category:parametric]]

	==Description==		==Description==

Himpe at 11:36, 25 March 2013

2013-03-25T11:36:04Z

← Older revision		Revision as of 11:36, 25 March 2013
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	[[Category:parametric method]]		[[Category:parametric method]]

			==Description==

	The model reduction method we present here is applicable to linear parameter-varying (LPV) systems of the form		The model reduction method we present here is applicable to linear parameter-varying (LPV) systems of the form
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	of Bilinear and Stochastic Systems, SIAM J. Cont. Optim., 49 (2011), pp. 686-711.		of Bilinear and Stochastic Systems, SIAM J. Cont. Optim., 49 (2011), pp. 686-711.

	Contact ~~information:~~		==Contact==

	'' [[User:breiten\|Tobias Breiten]]''		'' [[User:breiten\|Tobias Breiten]]''

Lnor at 11:57, 29 November 2012

2012-11-29T11:57:30Z

← Older revision		Revision as of 11:57, 29 November 2012
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	'' [[User:breiten\|Tobias Breiten]]''		'' [[User:breiten\|Tobias Breiten]]''
	~~[[Vertical Stand]]~~

Lnor at 11:56, 29 November 2012

2012-11-29T11:56:02Z

← Older revision		Revision as of 11:56, 29 November 2012
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	'' [[User:breiten\|Tobias Breiten]]''		'' [[User:breiten\|Tobias Breiten]]''
			[[Vertical Stand]]

Breiten at 08:21, 26 November 2012

2012-11-26T08:21:45Z

← Older revision		Revision as of 08:21, 26 November 2012
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	For a detailed analysis of this approach, we refer to e.g. [3]. Another possibility is to aim at a model reduction method which is optimal with respect to a certain system norm. In [1], the authors investigate a possible extension of the linear <math>H_2</math>-norm and propose an algorithm which extends the well-known iterative rational Krylov algorithm (IRKA) to the bilinear setting specified above.		For a detailed analysis of this approach, we refer to e.g. [3]. Another possibility is to aim at a model reduction method which is optimal with respect to a certain system norm. In [1], the authors investigate a possible extension of the linear <math>H_2</math>-norm and propose an algorithm which extends the well-known iterative rational Krylov algorithm (IRKA) to the bilinear setting specified above.

	Both methods have been tested on several LPV control systems and seem to be a reasonable alternative to existing parametric model reduction methods.		Both methods have been tested on several LPV control systems (e.g., [[Microthruster_Unit\|Microthruster Unit]] and [[Scanning_Electrochemical_Microscopy\|Scanning Electrochemical Microscopy]]) and seem to be a reasonable alternative to existing parametric model reduction methods.

Breiten: /* References */

2012-11-19T08:08:20Z

References

← Older revision		Revision as of 08:08, 19 November 2012
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	Contact information:		Contact information:

	'' [[User:breiten]]''		'' [[User:breiten\|Tobias Breiten]]''

Breiten: /* References */

2012-11-19T08:06:52Z

References

← Older revision		Revision as of 08:06, 19 November 2012
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	[3] P. Benner and T. Damm, Lyapunov Equations, Energy Functionals, and Model Order Reduction		[3] P. Benner and T. Damm, Lyapunov Equations, Energy Functionals, and Model Order Reduction
	of Bilinear and Stochastic Systems, SIAM J. Cont. Optim., 49 (2011), pp. 686-711.		of Bilinear and Stochastic Systems, SIAM J. Cont. Optim., 49 (2011), pp. 686-711.

			Contact information:

			'' [[User:breiten]]''

Will at 15:37, 8 December 2011

2011-12-08T15:37:47Z

← Older revision		Revision as of 15:37, 8 December 2011
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			[[Category:method]]
			[[Category:non-linear method]]
			[[Category:parametric method]]


	The model reduction method we present here is applicable to linear parameter-varying (LPV) systems of the form		The model reduction method we present here is applicable to linear parameter-varying (LPV) systems of the form