M.D. Doan, T. Keviczky, and B. De Schutter, "A hierarchical MPC approach with guaranteed feasibility for dynamically coupled linear systems," in Distributed Model Predictive Control Made Easy (R.R. Negenborn and J.M. Maestre, eds.), vol. 69 of Intelligent Systems, Control and Automation: Science and Engineering, Dordrecht, The Netherlands: Springer, ISBN 978-94-007-7005-8, pp. 393-406, 2014.
In this chapter we describe an iterative two-layer hierarchical approach to MPC of large-scale linear systems subject to coupled linear constraints. The algorithm uses constraint tightening and applies a primal-dual iterative averaging procedure to provide feasible solutions in every sampling step. This helps overcome typical practical issues related to the asymptotic convergence of dual decomposition based distributed MPC approaches. Bounds on constraint violation and level of suboptimality are provided. The method can be applied to large-scale MPC problems that are feasible in the first sampling step and for which the Slater condition holds (i.e., there exists a solution that strictly satisfies the inequality constraints). Using this method, the controller can generate feasible solutions of the MPC problem even when the dual solution does not reach optimality, and closed-loop stability is also ensured using bounded suboptimality.