Integrating Bayesian methods with neural network--based model predictive control: a review

TL;DR

This review assesses how Bayesian methods are embedded in neural network–based model predictive control to quantify and propagate uncertainty. It surveys application domains, NN architectures, and control formulations, analyzes reported gains and reliability, and highlights methodological diversity and gaps. The findings suggest Bayesian approaches can improve robustness but gains are dataset- and baseline-dependent, with limited extrapolation testing. The authors advocate standardized benchmarks, ablation studies, and transparent reporting to rigorously determine the practical value of Bayesian techniques for MPC.

Abstract

In this review, we assess the use of Bayesian methods in model predictive control (MPC), focusing on neural-network-based modeling, control design, and uncertainty quantification. We systematically analyze individual studies and how they are implemented in practice. While Bayesian approaches are increasingly adopted to capture and propagate uncertainty in MPC, reported gains in performance and robustness remain fragmented, with inconsistent baselines and limited reliability analyses. We therefore argue for standardized benchmarks, ablation studies, and transparent reporting to rigorously determine the effectiveness of Bayesian techniques for MPC.

Figures (3)

• Figure 1: Number of articles by country
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• Figure 3: Percentage share of application areas