Computation of the frequency responses for distributed systems with one spatial variable

Binh K. Lieu; Mihailo R. Jovanović

doi:10.1109/CDC.2011.6161523

Computation of the frequency responses for distributed systems with one spatial variable

Binh K. Lieu
, Mihailo R. Jovanović

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

3 Scopus citations

Abstract

For a class of distributed systems with one spatial variable, we develop a method for computing the maximum singular value of the frequency response operator. This computation is typically done by resorting to finite-dimensional approximations of the underlying operators. In this paper, we introduce an alternative approach that avoids the need for numerical approximation of the operators in the evolution model. This involves two steps: (i) recasting the frequency response operator as a two point boundary value problem; and (ii) using state-of-the-art automatic spectral collocation techniques for solving the resulting boundary value problems with accuracy comparable to machine precision. We provide an example from viscoelastic fluid dynamics to illustrate the utility of the proposed method.

Original language	English (US)
Title of host publication	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6956-6961
Number of pages	6
ISBN (Print)	9781612848006
DOIs	https://doi.org/10.1109/CDC.2011.6161523
State	Published - 2011
Event	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States Duration: Dec 12 2011 → Dec 15 2011

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Country/Territory	United States
City	Orlando, FL
Period	12/12/11 → 12/15/11

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10.1109/CDC.2011.6161523

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Lieu, B. K., & Jovanović, M. R. (2011). Computation of the frequency responses for distributed systems with one spatial variable. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 (pp. 6956-6961). Article 6161523 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2011.6161523

Computation of the frequency responses for distributed systems with one spatial variable. / Lieu, Binh K.; Jovanović, Mihailo R.
2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. Institute of Electrical and Electronics Engineers Inc., 2011. p. 6956-6961 6161523 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Lieu, BK & Jovanović, MR 2011, Computation of the frequency responses for distributed systems with one spatial variable. in 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011., 6161523, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 6956-6961, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6161523

Lieu BK, Jovanović MR. Computation of the frequency responses for distributed systems with one spatial variable. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. Institute of Electrical and Electronics Engineers Inc. 2011. p. 6956-6961. 6161523. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2011.6161523

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abstract = "For a class of distributed systems with one spatial variable, we develop a method for computing the maximum singular value of the frequency response operator. This computation is typically done by resorting to finite-dimensional approximations of the underlying operators. In this paper, we introduce an alternative approach that avoids the need for numerical approximation of the operators in the evolution model. This involves two steps: (i) recasting the frequency response operator as a two point boundary value problem; and (ii) using state-of-the-art automatic spectral collocation techniques for solving the resulting boundary value problems with accuracy comparable to machine precision. We provide an example from viscoelastic fluid dynamics to illustrate the utility of the proposed method.",

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AB - For a class of distributed systems with one spatial variable, we develop a method for computing the maximum singular value of the frequency response operator. This computation is typically done by resorting to finite-dimensional approximations of the underlying operators. In this paper, we introduce an alternative approach that avoids the need for numerical approximation of the operators in the evolution model. This involves two steps: (i) recasting the frequency response operator as a two point boundary value problem; and (ii) using state-of-the-art automatic spectral collocation techniques for solving the resulting boundary value problems with accuracy comparable to machine precision. We provide an example from viscoelastic fluid dynamics to illustrate the utility of the proposed method.

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Computation of the frequency responses for distributed systems with one spatial variable

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