On the convergence rate of a Jacobi algorithm for Cooperative Distributed MPC

This paper investigates the convergence of an iterative distributed model predictive control (DMPC) scheme for linear systems interconnected by dynamics and costs. The DMPC scheme is based on a Jacobi-type iteration and exchange of primal variables. Previous results show that, in the limit, the scheme converges to the Pareto optimal solution but no results on the convergence rate are given. We will first establish a bound on the convergence rate and show that weights used in the scheme and strength of coupling between subsystems have a strong influence on this bound. Subsequently, two approaches to determine the weights are compared. Random numerical examples are used to compare the theoretical bound on the convergence rate with the actual convergence of the scheme.