M.D. Doan, T. Keviczky, and B. De Schutter, "A distributed optimization-based approach for hierarchical model predictive control of large-scale systems with coupled dynamics and constraints: Extended report," Tech. rep. 11-039, Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands, 8 pp., Aug. 2011. A short version of this paper has been published in the Proceedings of the 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), Orlando, Florida, pp. 5236-5241, Dec. 2011.
We present a hierarchical model predictive control approach for large-scale systems based on dual decomposition. The proposed scheme allows coupling in both dynamics and constraints between the subsystems and generates a primal feasible solution within a finite number of iterations, using primal averaging and a constraint tightening approach. The primal update is performed in a distributed way and does not require exact solutions, while the dual problem uses an approximate subgradient method. Stability of the scheme is established using bounded suboptimality.