Distributed Model Predictive Consensus via the Alternating Direction Method of Multipliers

We propose a distributed optimization method for solving a distributed model predictive consensus problem. The goal is to design a distributed controller for a network of dynamical systems to optimize a coupled objective function while respecting state and input constraints. The distributed optimization method is an augmented Lagrangian method called the Alternating Direction Method of Multipliers (ADMM), which was introduced in the 1970s but has seen a recent resurgence in the context of dramatic increases in computing power and the development of widely available distributed computing platforms. The method is applied to position and velocity consensus in a network of double integrators. We find that a few tens of ADMM iterations yield closed-loop performance near what is achieved by solving the optimization problem centrally. Furthermore, the use of recent code generation techniques for solving local subproblems yields fast overall computation times.

💡 Research Summary

The paper tackles the problem of achieving consensus among a network of dynamical agents while respecting state and input constraints, using a distributed model predictive control (MPC) framework. Traditional centralized MPC requires gathering all agents’ states, solving a single large‑scale optimization problem, and then broadcasting the control actions. This approach quickly becomes computationally prohibitive and creates a heavy communication burden as the number of agents grows. To overcome these limitations, the authors adopt the Alternating Direction Method of Multipliers (ADMM), an augmented‑Lagrangian technique originally introduced in the 1970s but recently revived thanks to advances in parallel computing and the availability of distributed processing platforms.

Problem formulation
Each agent is modeled as a double integrator with state (x_i =