A Homogeneous and Self-Dual Interior-Point Linear Programming Algorithm for Economic Model Predictive Control

Leo Emil Sokoler; Gianluca Frison; Anders Skajaa; Rasmus Fogtmann Halvgaard; John Bagterp Jørgensen

doi:10.1109/TAC.2015.2495558

A Homogeneous and Self-Dual Interior-Point Linear Programming Algorithm for Economic Model Predictive Control

Leo Emil Sokoler, Gianluca Frison, Anders Skajaa, Rasmus Fogtmann Halvgaard, John Bagterp Jørgensen

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Abstract

We develop an efficient homogeneous and self-dual interior-point method (IPM) for the linear programs arising in economic model predictive control of constrained linear systems with linear objective functions. The algorithm is based on a Riccati iteration procedure, which is adapted to the linear system of equations solved in homogeneous and self-dual IPMs. Fast convergence is further achieved using a warm-start strategy. We implement the algorithm in MATLAB and C. Its performance is tested using a conceptual power management case study. Closed loop simulations show that 1) the proposed algorithm is significantly faster than several state-of-the-art IPMs based on sparse linear algebra, and 2) warm-start reduces the average number of iterations by 35-40%.

Original language	English
Journal	I E E E Transactions on Automatic Control
Volume	PP
Issue number	99
Number of pages	6
ISSN	0018-9286
DOIs	https://doi.org/10.1109/TAC.2015.2495558
Publication status	Published - 2015

Keywords

Optimization algorithms
Linear programming algorithms
Predictive control for linear systems
Riccati iterations
Energy systems

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title = "A Homogeneous and Self-Dual Interior-Point Linear Programming Algorithm for Economic Model Predictive Control",

abstract = "We develop an efficient homogeneous and self-dual interior-point method (IPM) for the linear programs arising in economic model predictive control of constrained linear systems with linear objective functions. The algorithm is based on a Riccati iteration procedure, which is adapted to the linear system of equations solved in homogeneous and self-dual IPMs. Fast convergence is further achieved using a warm-start strategy. We implement the algorithm in MATLAB and C. Its performance is tested using a conceptual power management case study. Closed loop simulations show that 1) the proposed algorithm is significantly faster than several state-of-the-art IPMs based on sparse linear algebra, and 2) warm-start reduces the average number of iterations by 35-40%.",

keywords = "Optimization algorithms, Linear programming algorithms, Predictive control for linear systems, Riccati iterations, Energy systems",

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AU - Sokoler, Leo Emil

AU - Frison, Gianluca

AU - Skajaa, Anders

AU - Halvgaard, Rasmus Fogtmann

AU - Jørgensen, John Bagterp

PY - 2015

Y1 - 2015

N2 - We develop an efficient homogeneous and self-dual interior-point method (IPM) for the linear programs arising in economic model predictive control of constrained linear systems with linear objective functions. The algorithm is based on a Riccati iteration procedure, which is adapted to the linear system of equations solved in homogeneous and self-dual IPMs. Fast convergence is further achieved using a warm-start strategy. We implement the algorithm in MATLAB and C. Its performance is tested using a conceptual power management case study. Closed loop simulations show that 1) the proposed algorithm is significantly faster than several state-of-the-art IPMs based on sparse linear algebra, and 2) warm-start reduces the average number of iterations by 35-40%.

AB - We develop an efficient homogeneous and self-dual interior-point method (IPM) for the linear programs arising in economic model predictive control of constrained linear systems with linear objective functions. The algorithm is based on a Riccati iteration procedure, which is adapted to the linear system of equations solved in homogeneous and self-dual IPMs. Fast convergence is further achieved using a warm-start strategy. We implement the algorithm in MATLAB and C. Its performance is tested using a conceptual power management case study. Closed loop simulations show that 1) the proposed algorithm is significantly faster than several state-of-the-art IPMs based on sparse linear algebra, and 2) warm-start reduces the average number of iterations by 35-40%.

KW - Optimization algorithms

KW - Linear programming algorithms

KW - Predictive control for linear systems

KW - Riccati iterations

KW - Energy systems

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DO - 10.1109/TAC.2015.2495558

M3 - Journal article

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VL - PP

JO - I E E E Transactions on Automatic Control

JF - I E E E Transactions on Automatic Control

IS - 99

ER -

A Homogeneous and Self-Dual Interior-Point Linear Programming Algorithm for Economic Model Predictive Control

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