Title: 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.