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

L. E. Sokoler, G. Frison, A. Skajaa, R. Halvgaard, and J. B. Jørgensen

Abstract

We develop an efficient homogeneous and self-dual interior-point method (IPM) for the linear programs arising in economic model predictive control (MPC) 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 by means of a recent warm-start strategy for homogeneous and self-dual IPMs. 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%.

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Reference

L. E. Sokoler, G. Frison, A. Skajaa, R. Halvgaard, and J. B. Jørgensen “A Homogeneous and Self-Dual Interior-Point Linear Programming Algorithm for Economic Model Predictive Control”, IEEE Transactions on Automatic Control, submitted, 2013.