Distributed and Localized Closed Loop Model Predictive Control via System Level Synthesis

We present the Distributed and Localized Model Predictive Control (DLMPC) algorithm for large-scale structured linear systems, a distributed closed loop model predictive control scheme wherein only local state and model information needs to be exchanged between subsystems for the computation and implementation of control actions. We use the System Level Synthesis (SLS) framework to reformulate the centralized MPC problem as an optimization problem over closed loop system responses, and show that this allows us to naturally impose localized communication constraints between sub-controllers. We show that the structure of the resulting optimization problem can be exploited to develop an Alternating Direction Method of Multipliers (ADMM) based algorithm that allows for distributed and localized computation of distributed closed loop control policies. We conclude with numerical simulations to demonstrate the usefulness of our method, in which we show that the computational complexity of the subproblems solved by each subsystem in DLMPC is independent of the size of the global system. To the best of our knowledge, DLMPC is the first MPC algorithm that allows for the scalable distributed computation of distributed closed loop control policies.