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This paper presents a distributed stochastic model predictive control (SMPC)approach for large-scale linear systems with private and common uncertaintiesin a plug-and-play framework. Using the so-called scenario approach, thecentralized SMPC involves formulating a large-scale finite-horizon scenariooptimization problem at each sampling time, which is in general computationallydemanding, due to the large number of required scenarios. We present two novelideas in this paper to address this issue. We first develop a technique todecompose the large-scale scenario program into distributed scenario programsthat exchange a certain number of scenarios with each other in order to computelocal decisions using the alternating direction method of multipliers (ADMM).We show the exactness of the decomposition with a-priori probabilisticguarantees for the desired level of constraint fulfillment for both uncertaintysources. As our second contribution, we develop an inter-agent softcommunication scheme based on a set parametrization technique together with thenotion of probabilistically reliable sets to reduce the required communicationbetween the subproblems. We show how to incorporate the probabilisticreliability notion into existing results and provide new guarantees for thedesired level of constraint violations. Two different simulation studies of twotypes of systems interactions, dynamically coupled and coupling constraints,are presented to illustrate the advantages of the proposed framework.

Distributed Stochastic Model Predictive Control for Large-Scale Linear Systems with Private and Common Uncertainty Sources