Distributed Model Predictive Control of linear discrete-time systems with coupled constraints

This paper proposes a Distributed Model Predictive Control (DMPC) approach for a family of discrete-time linear systems with local (uncoupled) and global (coupled) constraints. The proposed approach is based on the dual problem of an overall MPC optimization problem involving all systems. This dual problem is then solved distributively by converting it into a consensus problem for the dual variables associated with the coupled constraints. As the state of convergence is difficult to ascertain, the distributed consensus algorithm yields an inexact solution. By the tightening of the coupled constraints, but not the local constraints, it is still possible to ensure recursive feasibility and exponential stability of the overall closed-loop system. The approach requires that the network of systems be connected and hence, local communications among the systems are needed. The performance of the proposed approach is demonstrated by a numerical example.