Polynomial Chaos-based Stochastic Model Predictive Control: An Overview and Future Research Directions

TL;DR

This paper reviews how Polynomial Chaos Theory enhances stochastic model predictive control by improving uncertainty propagation and reducing computational complexity, with a focus on future research directions.

Contribution

It provides a comprehensive overview of applying Polynomial Chaos Theory to stochastic MPC, highlighting its benefits and potential for future developments.

Findings

PCT enables accurate uncertainty propagation in nonlinear systems.

PCT reduces computational complexity in SMPC.

The paper discusses future research directions in PCT-based SMPC.

Abstract

This article is devoted to providing a review of mathematical formulations in which Polynomial Chaos Theory (PCT) has been incorporated into stochastic model predictive control (SMPC). In the past decade, PCT has been shown to provide a computationally tractable way to perform complete and accurate uncertainty propagation through (smooth) nonlinear dynamic systems. As such, it represents a very useful computational tool for accelerating the computations needed in SMPC with time invariant uncertainties. It turns out that it can also be used to reduce complexity of chance constraints, which are an important component of SMPC. In this paper, we provide an overview of PCT and discuss how it can be applied in such time invariant settings.