A Dantzig-Wolfe Decomposition Algorithm for Linear Economic Model Predictive Control of Dynamically Decoupled Subsystems

L. E. Sokoler, L. Standardi, K. Edlund, N. K. Poulsen, H. Madsen, and J. B. Jørgensen

Abstract

This paper presents a warm-started Dantzig-Wolfe decomposition algorithm tailored to economic model predictive control of dynamically decoupled subsystems. We formulate the constrained optimal control problem solved at each sampling instant as a linear program with state space constraints, input limits, input rate limits, and soft output limits. The objective function of the linear program is related directly to the cost of operating the subsystems, and the cost of violating the soft output constraints. Simulations for large-scale economic power dispatch problems show that the proposed algorithm is favorable over both state-ofthe- art linear programming solvers, and a structure exploiting implementation of the alternating direction method of multipliers. It is also demonstrated that the control strategy presented in this paper can be tuned using a weighted l1-regularization term. In the presence of process and measurement noise, such a regularization term is critical for achieving the desired closed-loop performance.

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Reference

L. E. Sokoler, L. Standardi, K. Edlund, N. K. Poulsen, H. Madsen, and J. B. Jørgensen “A Dantzig-Wolfe Decomposition Algorithm for Linear Economic Model Predictive Control of Dynamically Decoupled Subsystems”, Journal of Process Control (SI: Economic MPC), accepted, 2014.