A simple condition for the convexity of optimal control over networks with delays

Michael Rotkowitz; Randy Cogill; Sanjay Lall

doi:10.1109/CDC.2005.1583236

A simple condition for the convexity of optimal control over networks with delays

Michael Rotkowitz^*, Randy Cogill, Sanjay Lall

^*Corresponding author for this work

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

20 Citations (Scopus)

Abstract

We consider the problem of multiple subsystems, each with Its own controller, such that the dynamics of each subsystem may affect those of other subsystems with some propagation delays, and the controllers may communicate with each other with some transmission delays. We wish to synthesize controllers to minimize a closed-loop norm for the entire system. We show that if the transmission delays satisfy the triangle inequality, then the simple condition that the transmission delay between any two subsystems is less than the propagation delay between those subsystems allows for the optimal control problem to be recast as a convex optimization problem.

Original language	English
Title of host publication	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages	6686-6691
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2005.1583236
Publication status	Published - 2005
Externally published	Yes
Event	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain Duration: 12 Dec 2005 → 15 Dec 2005

Publication series

Name	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume	2005

Conference

Conference	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Country/Territory	Spain
City	Seville
Period	12/12/05 → 15/12/05

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10.1109/CDC.2005.1583236

Cite this

Rotkowitz, M., Cogill, R., & Lall, S. (2005). A simple condition for the convexity of optimal control over networks with delays. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (pp. 6686-6691). Article 1583236 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005). https://doi.org/10.1109/CDC.2005.1583236

Rotkowitz, Michael ; Cogill, Randy ; Lall, Sanjay. / A simple condition for the convexity of optimal control over networks with delays. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. pp. 6686-6691 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05).

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title = "A simple condition for the convexity of optimal control over networks with delays",

abstract = "We consider the problem of multiple subsystems, each with Its own controller, such that the dynamics of each subsystem may affect those of other subsystems with some propagation delays, and the controllers may communicate with each other with some transmission delays. We wish to synthesize controllers to minimize a closed-loop norm for the entire system. We show that if the transmission delays satisfy the triangle inequality, then the simple condition that the transmission delay between any two subsystems is less than the propagation delay between those subsystems allows for the optimal control problem to be recast as a convex optimization problem.",

author = "Michael Rotkowitz and Randy Cogill and Sanjay Lall",

year = "2005",

doi = "10.1109/CDC.2005.1583236",

language = "English",

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series = "Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05",

pages = "6686--6691",

booktitle = "Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05",

note = "44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 ; Conference date: 12-12-2005 Through 15-12-2005",

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Rotkowitz, M, Cogill, R & Lall, S 2005, A simple condition for the convexity of optimal control over networks with delays. in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05., 1583236, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, vol. 2005, pp. 6686-6691, 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, Seville, Spain, 12/12/05. https://doi.org/10.1109/CDC.2005.1583236

A simple condition for the convexity of optimal control over networks with delays. / Rotkowitz, Michael; Cogill, Randy; Lall, Sanjay.
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 6686-6691 1583236 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005).

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

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AU - Lall, Sanjay

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N2 - We consider the problem of multiple subsystems, each with Its own controller, such that the dynamics of each subsystem may affect those of other subsystems with some propagation delays, and the controllers may communicate with each other with some transmission delays. We wish to synthesize controllers to minimize a closed-loop norm for the entire system. We show that if the transmission delays satisfy the triangle inequality, then the simple condition that the transmission delay between any two subsystems is less than the propagation delay between those subsystems allows for the optimal control problem to be recast as a convex optimization problem.

AB - We consider the problem of multiple subsystems, each with Its own controller, such that the dynamics of each subsystem may affect those of other subsystems with some propagation delays, and the controllers may communicate with each other with some transmission delays. We wish to synthesize controllers to minimize a closed-loop norm for the entire system. We show that if the transmission delays satisfy the triangle inequality, then the simple condition that the transmission delay between any two subsystems is less than the propagation delay between those subsystems allows for the optimal control problem to be recast as a convex optimization problem.

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Rotkowitz M, Cogill R, Lall S. A simple condition for the convexity of optimal control over networks with delays. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 6686-6691. 1583236. (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05). doi: 10.1109/CDC.2005.1583236

A simple condition for the convexity of optimal control over networks with delays

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