Distributed Stochastic Model Predictive Control for dynamically coupled Linear Systems using Probabilistic Reachable Sets

In this paper, we propose a stochastic model predictive control (MPC) algorithm for linear distributed discrete-time systems affected by unbounded additive Gaussian disturbances, which are subject to local probabilistic constraints. Probabilistic constraints are treated with the concept of probabili...

Full description

Saved in:
Bibliographic Details
Published in2019 18th European Control Conference (ECC) pp. 1362 - 1367
Main Authors Mark, Christoph, Liu, Steven
Format Conference Proceeding
LanguageEnglish
Published EUCA 01.06.2019
Subjects
Additives
Covariance matrices
Linear systems
Numerical stability
Prediction algorithms
Predictive control
Probabilistic logic
Stability analysis
Stochastic processes
Upper bound
Online AccessGet full text
DOI10.23919/ECC.2019.8796188

Cover

More Information
Summary:In this paper, we propose a stochastic model predictive control (MPC) algorithm for linear distributed discrete-time systems affected by unbounded additive Gaussian disturbances, which are subject to local probabilistic constraints. Probabilistic constraints are treated with the concept of probabilistic reachable sets, which are an analogy to robust reachable sets for robust MPC. We present a method which decouples the global covariance matrix into a block diagonal upper bound. Together with the decomposition of the centralized problem, we define local probabilistic invariant sets as terminal regions, where we additionally derive a condition that gives us a probabilistic guarantee of invariance. We demonstrate our approach on an example, highlighting the closed-loop performance and constraint satisfaction compared to a centralized scheme.
DOI:10.23919/ECC.2019.8796188