A Decomposition Algorithm for Mean-Variance Economic Model Predictive Control of Stochastic Linear Systems

Leo Emil Sokoler; Bernd Dammann; Henrik Madsen; John Bagterp Jørgensen

doi:10.1109/ISIC.2014.6967612

A Decomposition Algorithm for Mean-Variance Economic Model Predictive Control of Stochastic Linear Systems

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

Abstract

This paper presents a decomposition algorithm for solving the optimal control problem (OCP) that arises in Mean-Variance Economic Model Predictive Control of stochastic linear systems. The algorithm applies the alternating direction method of multipliers to a reformulation of the OCP that decomposes into small independent subproblems. We test the decomposition algorithm using a simple power management case study, in which the OCP is formulated as a convex quadratic program. Simulations show that the decomposition algorithm scales linearly in the number of uncertainty scenarios. Moreover, a parallel implementation of the algorithm is several orders of magnitude faster than state-of-the-art convex quadratic programming algorithms, provided that the number of uncertainty scenarios is large.

Original language	English
Title of host publication	Proceedings of the IEEE International Symposium on Intelligent Control (ISIC) 2014, Part of 2014 IEEE Multi-conference on Systems and Control
Publisher	IEEE
Publication date	2014
Pages	1086-1093
ISBN (Electronic)	978-1-4799-7406-1
DOIs	https://doi.org/10.1109/ISIC.2014.6967612
Publication status	Published - 2014
Event	2014 IEEE Multi-Conference on Systems and Control - Antibes Congress Center, Antibes, France Duration: 8 Oct 2014 → 10 Oct 2014 http://www.msc2014.org/

Conference

Conference	2014 IEEE Multi-Conference on Systems and Control
Location	Antibes Congress Center
Country/Territory	France
City	Antibes
Period	08/10/2014 → 10/10/2014
Other	Also include the IEEE International Symposium on Intelligent Control (ISIC) 2014
Internet address	http://www.msc2014.org/

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Sokoler, L. E., Dammann, B., Madsen, H., & Jørgensen, J. B. (2014). A Decomposition Algorithm for Mean-Variance Economic Model Predictive Control of Stochastic Linear Systems. In Proceedings of the IEEE International Symposium on Intelligent Control (ISIC) 2014, Part of 2014 IEEE Multi-conference on Systems and Control (pp. 1086-1093). IEEE. https://doi.org/10.1109/ISIC.2014.6967612

@inproceedings{ed60872a8be142bf9ee3f4f46c873f46,

title = "A Decomposition Algorithm for Mean-Variance Economic Model Predictive Control of Stochastic Linear Systems",

abstract = "This paper presents a decomposition algorithm for solving the optimal control problem (OCP) that arises in Mean-Variance Economic Model Predictive Control of stochastic linear systems. The algorithm applies the alternating direction method of multipliers to a reformulation of the OCP that decomposes into small independent subproblems. We test the decomposition algorithm using a simple power management case study, in which the OCP is formulated as a convex quadratic program. Simulations show that the decomposition algorithm scales linearly in the number of uncertainty scenarios. Moreover, a parallel implementation of the algorithm is several orders of magnitude faster than state-of-the-art convex quadratic programming algorithms, provided that the number of uncertainty scenarios is large.",

author = "Sokoler, \{Leo Emil\} and Bernd Dammann and Henrik Madsen and J{\o}rgensen, \{John Bagterp\}",

year = "2014",

doi = "10.1109/ISIC.2014.6967612",

language = "English",

pages = "1086--1093",

booktitle = "Proceedings of the IEEE International Symposium on Intelligent Control (ISIC) 2014, Part of 2014 IEEE Multi-conference on Systems and Control",

publisher = "IEEE",

address = "United States",

note = "2014 IEEE Multi-Conference on Systems and Control, MSC 2014 ; Conference date: 08-10-2014 Through 10-10-2014",

url = "http://www.msc2014.org/",

}

Sokoler, LE, Dammann, B , Madsen, H & Jørgensen, JB 2014, A Decomposition Algorithm for Mean-Variance Economic Model Predictive Control of Stochastic Linear Systems. in Proceedings of the IEEE International Symposium on Intelligent Control (ISIC) 2014, Part of 2014 IEEE Multi-conference on Systems and Control. IEEE, pp. 1086-1093, 2014 IEEE Multi-Conference on Systems and Control, Antibes, France, 08/10/2014. https://doi.org/10.1109/ISIC.2014.6967612

A Decomposition Algorithm for Mean-Variance Economic Model Predictive Control of Stochastic Linear Systems. / Sokoler, Leo Emil; Dammann, Bernd ; Madsen, Henrik et al.
Proceedings of the IEEE International Symposium on Intelligent Control (ISIC) 2014, Part of 2014 IEEE Multi-conference on Systems and Control. IEEE, 2014. p. 1086-1093.

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

TY - GEN

T1 - A Decomposition Algorithm for Mean-Variance Economic Model Predictive Control of Stochastic Linear Systems

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AU - Dammann, Bernd

AU - Madsen, Henrik

AU - Jørgensen, John Bagterp

PY - 2014

Y1 - 2014

N2 - This paper presents a decomposition algorithm for solving the optimal control problem (OCP) that arises in Mean-Variance Economic Model Predictive Control of stochastic linear systems. The algorithm applies the alternating direction method of multipliers to a reformulation of the OCP that decomposes into small independent subproblems. We test the decomposition algorithm using a simple power management case study, in which the OCP is formulated as a convex quadratic program. Simulations show that the decomposition algorithm scales linearly in the number of uncertainty scenarios. Moreover, a parallel implementation of the algorithm is several orders of magnitude faster than state-of-the-art convex quadratic programming algorithms, provided that the number of uncertainty scenarios is large.

AB - This paper presents a decomposition algorithm for solving the optimal control problem (OCP) that arises in Mean-Variance Economic Model Predictive Control of stochastic linear systems. The algorithm applies the alternating direction method of multipliers to a reformulation of the OCP that decomposes into small independent subproblems. We test the decomposition algorithm using a simple power management case study, in which the OCP is formulated as a convex quadratic program. Simulations show that the decomposition algorithm scales linearly in the number of uncertainty scenarios. Moreover, a parallel implementation of the algorithm is several orders of magnitude faster than state-of-the-art convex quadratic programming algorithms, provided that the number of uncertainty scenarios is large.

U2 - 10.1109/ISIC.2014.6967612

DO - 10.1109/ISIC.2014.6967612

M3 - Article in proceedings

SP - 1086

EP - 1093

BT - Proceedings of the IEEE International Symposium on Intelligent Control (ISIC) 2014, Part of 2014 IEEE Multi-conference on Systems and Control

PB - IEEE

T2 - 2014 IEEE Multi-Conference on Systems and Control

Y2 - 8 October 2014 through 10 October 2014

ER -

A Decomposition Algorithm for Mean-Variance Economic Model Predictive Control of Stochastic Linear Systems

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