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Model Predictive Control (MPC) for {networked, cyber-physical, multi-agent} systems requires numerical methods to solve optimal control problems while meeting communication and real-time requirements. This paper presents an introduction on six distributed optimization algorithms and compares their properties in the context of distributed MPC for linear systems with convex quadratic objectives and polytopic constraints. In particular, dual decomposition, the alternating direction method of multipliers, a distributed active set method, an essentially decentralized interior point method, and Jacobi iterations are discussed. Numerical examples illustrate the challenges, the prospect, and the limits of distributed MPC with inexact solutions.

A compendium of optimization algorithms for distributed linear-quadratic MPC