Cooperative Distributed Model Predictive Control via Linear Programming★A Divide and Conquer Approach*

Motivated by the recent progress in centralized Model Predictive Control (MPC) design using a linear program (LP) and distributed MPC with quadratic program (QP) formulations, this paper discusses the design of LP-based cooperative distributed MPC for large scale linear systems with coupled dynamics and decoupled input constraints. As such, we examine the applicability of the Divide and Conquer approach to QP-based cooperative distributed MPC, recently proposed by the authors, to the LP-based case. It is shown that within the Divide and Conquer framework, an upbound of the original LP-based cooperative cost function (instead of itself), can be optimized for computing local inputs, resulting in suboptimal policies. However, advantages of doing so include the independency of the computation of local inputs and a large amount of communication burden reduction, as guaranteed by theoretical analysis and illustrated through numerical simulation. We also present closed-loop stability analysis and point out some questions worth further investigation.