A stochastic MPC scheme for distributed systems with multiplicative uncertainty

TL;DR

This paper introduces a distributed stochastic MPC method for linear systems with multiplicative uncertainties, ensuring chance constraint satisfaction, recursive feasibility, and convergence through a distributed algorithm based on ADMM.

Contribution

It develops a fully distributed stochastic MPC scheme for systems with multiplicative uncertainties, incorporating chance constraints via Cantelli's inequality and ensuring recursive feasibility and convergence.

Findings

Successfully satisfies chance constraints in simulations

Demonstrates scalability and numerical efficiency

Ensures recursive feasibility and convergence

Abstract

This paper presents a Distributed Stochastic Model Predictive Control algorithm for networks of linear systems with multiplicative uncertainties and local chance constraints on the states and control inputs. The chance constraints are approximated via Cantelli's inequality by means of expected value and covariance. The cooperative control algorithm is based on the distributed Alternating Direction Method of Multipliers, which renders the controller fully distributedly implementable, recursively feasible and ensures point-wise convergence of the states. The aforementioned properties are guaranteed through a properly selected distributed invariant set and distributed terminal constraints for the mean and covariance. The paper closes with an example highlighting the chance constraint satisfaction, numerical properties and scalability of our approach.