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

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

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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10.1109/ISIC.2014.6967612

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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

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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.",

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

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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

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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.

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

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