Distributed Model Predictive Control of linear discrete-time systems with local and global 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 a MPC optimization problem involving all systems. This dual problem is then distributedly solved, based on the Alternating Direction Multiplier Method (ADMM) with several known simplifications. When the network of systems is large or sparsely connected, the computation of the optimal control using ADMM can be expensive. The proposed approach mitigates this problem by allowing early termination of the ADMM process. This is made possible via a finite-time consensus algorithm that determines the satisfaction of the termination condition and by appropriate tightening of the coupled constraints. Under reasonable assumptions, the approach is guaranteed to converge to a small neighborhood of the optimal so long as the network is connected. Recursive feasibility and exponential stability of the closed-loop system are shown. The performance of the proposed approach is demonstrated by a numerical example.