A compendium of optimization algorithms for distributed linear-quadratic MPC

Abstract 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 compares their properties in the context of MPC linear with convex quadratic objectives polytopic constraints. In particular, dual decomposition, alternating direction method multipliers, a active set method, essentially decentralized interior point Jacobi iterations are discussed. Numerical examples illustrate challenges, prospect, limits inexact solutions.