Synthesis of H2 optimal static structured controllers: Primal and dual formulations

Fu Lin; Makan Fardad; Mihailo R. Jovanovic

doi:10.1109/ALLERTON.2009.5394784

Synthesis of H₂ optimal static structured controllers: Primal and dual formulations

Fu Lin, Makan Fardad, Mihailo R. Jovanovic

Department of Electrical Engineering & Computer Science

Research output: Chapter in Book/Entry/Poem › Conference contribution

2 Scopus citations

Abstract

We consider the design of H₂ optimal static structured feedback gains for large-scale interconnected systems. The design of distributed controllers with access to measurements of a small number of the subsystems imposes particular sparsity constraints on the feedback gains. For this nonconvex constrained optimal control problem, we study both the primal and dual formulations to obtain optimality bounds. We exploit the sparsity structure present in large-scale systems by implementing an efficient quasi-Newton algorithm to solve the primal problem. We employ the subgradient method to solve the dual problem and obtain a lower bound for the optimal value of the performance index. Surprisingly, in many problems of practical interest, the upper bounds from solving primal problems and the lower bounds from solving dual problems are almost identical, suggesting the lack of duality gap in these applications and that the globally optimal structured gains have in fact been attained.

Original language	English (US)
Title of host publication	2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
Pages	340-346
Number of pages	7
DOIs	https://doi.org/10.1109/ALLERTON.2009.5394784
State	Published - 2009
Event	2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 - Monticello, IL, United States Duration: Sep 30 2009 → Oct 2 2009

Publication series

Name	2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009

Other

Other	2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
Country/Territory	United States
City	Monticello, IL
Period	9/30/09 → 10/2/09

Keywords

Decentralized control
Large-scale systems
Sparse matrices
Static feedback gains
Zero duality gap

ASJC Scopus subject areas

General Computer Science
Control and Systems Engineering
Communication

Access to Document

10.1109/ALLERTON.2009.5394784

Cite this

Lin, F., Fardad, M., & Jovanovic, M. R. (2009). Synthesis of H₂ optimal static structured controllers: Primal and dual formulations. In 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 (pp. 340-346). Article 5394784 (2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009). https://doi.org/10.1109/ALLERTON.2009.5394784

Synthesis of H₂ optimal static structured controllers: Primal and dual formulations. / Lin, Fu; Fardad, Makan; Jovanovic, Mihailo R.
2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009. 2009. p. 340-346 5394784 (2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009).

Research output: Chapter in Book/Entry/Poem › Conference contribution

Lin, F, Fardad, M & Jovanovic, MR 2009, Synthesis of H₂ optimal static structured controllers: Primal and dual formulations. in 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009., 5394784, 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009, pp. 340-346, 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009, Monticello, IL, United States, 9/30/09. https://doi.org/10.1109/ALLERTON.2009.5394784

Lin F, Fardad M, Jovanovic MR. Synthesis of H₂ optimal static structured controllers: Primal and dual formulations. In 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009. 2009. p. 340-346. 5394784. (2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009). doi: 10.1109/ALLERTON.2009.5394784

@inproceedings{145a5a81530d4e6abea1a389195e219e,

title = "Synthesis of H2 optimal static structured controllers: Primal and dual formulations",

abstract = "We consider the design of H2 optimal static structured feedback gains for large-scale interconnected systems. The design of distributed controllers with access to measurements of a small number of the subsystems imposes particular sparsity constraints on the feedback gains. For this nonconvex constrained optimal control problem, we study both the primal and dual formulations to obtain optimality bounds. We exploit the sparsity structure present in large-scale systems by implementing an efficient quasi-Newton algorithm to solve the primal problem. We employ the subgradient method to solve the dual problem and obtain a lower bound for the optimal value of the performance index. Surprisingly, in many problems of practical interest, the upper bounds from solving primal problems and the lower bounds from solving dual problems are almost identical, suggesting the lack of duality gap in these applications and that the globally optimal structured gains have in fact been attained.",

keywords = "Decentralized control, Large-scale systems, Sparse matrices, Static feedback gains, Zero duality gap",

author = "Fu Lin and Makan Fardad and Jovanovic, {Mihailo R.}",

year = "2009",

doi = "10.1109/ALLERTON.2009.5394784",

language = "English (US)",

isbn = "9781424458714",

series = "2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009",

pages = "340--346",

booktitle = "2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009",

note = "2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 ; Conference date: 30-09-2009 Through 02-10-2009",

}

TY - GEN

T1 - Synthesis of H2 optimal static structured controllers

T2 - 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009

AU - Lin, Fu

AU - Fardad, Makan

AU - Jovanovic, Mihailo R.

PY - 2009

Y1 - 2009

N2 - We consider the design of H2 optimal static structured feedback gains for large-scale interconnected systems. The design of distributed controllers with access to measurements of a small number of the subsystems imposes particular sparsity constraints on the feedback gains. For this nonconvex constrained optimal control problem, we study both the primal and dual formulations to obtain optimality bounds. We exploit the sparsity structure present in large-scale systems by implementing an efficient quasi-Newton algorithm to solve the primal problem. We employ the subgradient method to solve the dual problem and obtain a lower bound for the optimal value of the performance index. Surprisingly, in many problems of practical interest, the upper bounds from solving primal problems and the lower bounds from solving dual problems are almost identical, suggesting the lack of duality gap in these applications and that the globally optimal structured gains have in fact been attained.

AB - We consider the design of H2 optimal static structured feedback gains for large-scale interconnected systems. The design of distributed controllers with access to measurements of a small number of the subsystems imposes particular sparsity constraints on the feedback gains. For this nonconvex constrained optimal control problem, we study both the primal and dual formulations to obtain optimality bounds. We exploit the sparsity structure present in large-scale systems by implementing an efficient quasi-Newton algorithm to solve the primal problem. We employ the subgradient method to solve the dual problem and obtain a lower bound for the optimal value of the performance index. Surprisingly, in many problems of practical interest, the upper bounds from solving primal problems and the lower bounds from solving dual problems are almost identical, suggesting the lack of duality gap in these applications and that the globally optimal structured gains have in fact been attained.

KW - Decentralized control

KW - Large-scale systems

KW - Sparse matrices

KW - Static feedback gains

KW - Zero duality gap

UR - http://www.scopus.com/inward/record.url?scp=77949631239&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949631239&partnerID=8YFLogxK

U2 - 10.1109/ALLERTON.2009.5394784

DO - 10.1109/ALLERTON.2009.5394784

M3 - Conference contribution

AN - SCOPUS:77949631239

SN - 9781424458714

T3 - 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009

SP - 340

EP - 346

BT - 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009

Y2 - 30 September 2009 through 2 October 2009

ER -