Operator theoretic approach to the optimal distributed control problem for spatially invariant systems

Seddik M. Djouadi; Jin Dong

doi:10.1109/ACC.2015.7171128

Operator theoretic approach to the optimal distributed control problem for spatially invariant systems

Seddik M. Djouadi, Jin Dong

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

4 Scopus citations

Abstract

This paper considers the problem of optimal distributed control of spatially invariant systems. The Banach space duality structure of the problem is characterized in terms of tensor product spaces. This complements the prior study undertaken by the authors, where the dual and pre-dual formulations were in terms of abstract spaces. Here, we show that these spaces together with the pre-annihilator and annihilator subspaces can be realized explicitly as specific tensor spaces and subspaces, respectively. The tensor space formulation leads to a solution in terms of an operator given by a tensor product. Specifically, the optimal distributed control performance for spatially invariant systems is equal to the operator induced norm of this operator. The results obtained in this paper bridge the gap between control theory and the metric theory of tensor product spaces.

Original language	English
Title of host publication	ACC 2015 - 2015 American Control Conference
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2613-2618
Number of pages	6
ISBN (Electronic)	9781479986842
DOIs	https://doi.org/10.1109/ACC.2015.7171128
State	Published - Jul 28 2015
Externally published	Yes
Event	2015 American Control Conference, ACC 2015 - Chicago, United States Duration: Jul 1 2015 → Jul 3 2015

Publication series

Name	Proceedings of the American Control Conference
Volume	2015-July
ISSN (Print)	0743-1619

Conference

Conference	2015 American Control Conference, ACC 2015
Country/Territory	United States
City	Chicago
Period	07/1/15 → 07/3/15

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10.1109/ACC.2015.7171128

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Djouadi, S. M., & Dong, J. (2015). Operator theoretic approach to the optimal distributed control problem for spatially invariant systems. In ACC 2015 - 2015 American Control Conference (pp. 2613-2618). Article 7171128 (Proceedings of the American Control Conference; Vol. 2015-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2015.7171128

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title = "Operator theoretic approach to the optimal distributed control problem for spatially invariant systems",

abstract = "This paper considers the problem of optimal distributed control of spatially invariant systems. The Banach space duality structure of the problem is characterized in terms of tensor product spaces. This complements the prior study undertaken by the authors, where the dual and pre-dual formulations were in terms of abstract spaces. Here, we show that these spaces together with the pre-annihilator and annihilator subspaces can be realized explicitly as specific tensor spaces and subspaces, respectively. The tensor space formulation leads to a solution in terms of an operator given by a tensor product. Specifically, the optimal distributed control performance for spatially invariant systems is equal to the operator induced norm of this operator. The results obtained in this paper bridge the gap between control theory and the metric theory of tensor product spaces.",

author = "Djouadi, {Seddik M.} and Jin Dong",

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year = "2015",

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doi = "10.1109/ACC.2015.7171128",

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Djouadi, SM & Dong, J 2015, Operator theoretic approach to the optimal distributed control problem for spatially invariant systems. in ACC 2015 - 2015 American Control Conference., 7171128, Proceedings of the American Control Conference, vol. 2015-July, Institute of Electrical and Electronics Engineers Inc., pp. 2613-2618, 2015 American Control Conference, ACC 2015, Chicago, United States, 07/1/15. https://doi.org/10.1109/ACC.2015.7171128

Operator theoretic approach to the optimal distributed control problem for spatially invariant systems. / Djouadi, Seddik M.; Dong, Jin.
ACC 2015 - 2015 American Control Conference. Institute of Electrical and Electronics Engineers Inc., 2015. p. 2613-2618 7171128 (Proceedings of the American Control Conference; Vol. 2015-July).

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

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AU - Djouadi, Seddik M.

AU - Dong, Jin

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N2 - This paper considers the problem of optimal distributed control of spatially invariant systems. The Banach space duality structure of the problem is characterized in terms of tensor product spaces. This complements the prior study undertaken by the authors, where the dual and pre-dual formulations were in terms of abstract spaces. Here, we show that these spaces together with the pre-annihilator and annihilator subspaces can be realized explicitly as specific tensor spaces and subspaces, respectively. The tensor space formulation leads to a solution in terms of an operator given by a tensor product. Specifically, the optimal distributed control performance for spatially invariant systems is equal to the operator induced norm of this operator. The results obtained in this paper bridge the gap between control theory and the metric theory of tensor product spaces.

AB - This paper considers the problem of optimal distributed control of spatially invariant systems. The Banach space duality structure of the problem is characterized in terms of tensor product spaces. This complements the prior study undertaken by the authors, where the dual and pre-dual formulations were in terms of abstract spaces. Here, we show that these spaces together with the pre-annihilator and annihilator subspaces can be realized explicitly as specific tensor spaces and subspaces, respectively. The tensor space formulation leads to a solution in terms of an operator given by a tensor product. Specifically, the optimal distributed control performance for spatially invariant systems is equal to the operator induced norm of this operator. The results obtained in this paper bridge the gap between control theory and the metric theory of tensor product spaces.

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SP - 2613

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BT - ACC 2015 - 2015 American Control Conference

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2015 American Control Conference, ACC 2015

Y2 - 1 July 2015 through 3 July 2015

ER -

Operator theoretic approach to the optimal distributed control problem for spatially invariant systems

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