Sokoler, Leo Emil2; Standardi, Laura1; Edlund, Kristian5; Poulsen, Niels Kjølstad1; Madsen, Henrik1; Jørgensen, John Bagterp6
1 Department of Applied Mathematics and Computer Science, Technical University of Denmark2 Scientific Computing, Department of Applied Mathematics and Computer Science, Technical University of Denmark3 Dynamical Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark4 Center for Energy Resources Engineering, Center, Technical University of Denmark5 DONG Energy A/S6 Copenhagen Center for Health Technology, Center, Technical University of Denmark
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 significantly faster than both state-of-the-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 a well-behaved closed-loop performance.
Journal of Process Control, 2014, Vol 24, Issue 8, p. 1225-1236
Optimization; Dantzig–Wolfe decomposition; Regularization; Linear programming; Distributed model predictive control; Energy management