A distributed augmented Lagrangian method for model predictive control

In this paper we present a distributed Augmented Lagrangian (AL) algorithm to solve model predictive control (MPC) problems that involve a finite number of subsystems which interact with each other via a general network. We focus on discrete-time control systems with time-varying linear dynamics. Our method relies on the Accelerated Distributed Augmented Lagrangian (ADAL) algorithm, which can handle globally coupled linear constraints in a distributed manner based on a locally estimated AL. We prove that the theoretical complexity of ADAL to reach an ε-optimal solution both in terms of primal optimality gap and feasibility residual is O(1/ε) iterations. As suggested by our numerical analysis, ADAL achieves very fast convergence rates compared to the popular ADMM for distributed MPC.