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

Abstract: This paper presents a distributed stochastic model predictive control (SMPC) approach for large-scale linear systems with private and common uncertainties in a plug-and-play framework. Using the so-called scenario approach, the centralized SMPC involves formulating a large-scale finite-horizon scenario optimization problem at each sampling time, which is in general computationally demanding, due to the large number of required scenarios. We present two novel ideas in this paper to address this issue. We first develop a technique to decompose the large-scale scenario program into distributed scenario programs that exchange a certain number of scenarios with each other in order to compute local decisions using the alternating direction method of multipliers (ADMM). We show the exactness of the decomposition with a-priori probabilistic guarantees for the desired level of constraint fulfillment for both uncertainty sources. As our second contribution, we develop an inter-agent soft communication scheme based on a set parametrization technique together with the notion of probabilistically reliable sets to reduce the required communication between the subproblems. We show how to incorporate the probabilistic reliability notion into existing results and provide new guarantees for the desired level of constraint violations. Two different simulation studies of two types of systems interactions, dynamically coupled and coupling constraints, are presented to illustrate the advantages of the proposed framework.