Bayesian Learning Approach to Model Predictive Control

TL;DR

This paper integrates Bayesian learning with model predictive control, offering a unified framework that enhances control algorithm diversity and provides new insights into stochastic optimal control design.

Contribution

It combines Bayesian learning rules with model predictive control, bridging two frameworks and streamlining the understanding of control algorithm diversification.

Findings

Connects Bayesian learning with MPC, enriching control algorithm design.

Provides a variational formulation for diversified MPC algorithms.

Clarifies design choices through a Bayesian perspective.

Abstract

This study presents a Bayesian learning perspective towards model predictive control algorithms. High-level frameworks have been developed separately in the earlier studies on Bayesian learning and sampling-based model predictive control. On one hand, the Bayesian learning rule provides a general framework capable of generating various machine learning algorithms as special instances. On the other hand, the dynamic mirror descent model predictive control framework is capable of diversifying sample-rollout-based control algorithms. However, connections between the two frameworks have still not been fully appreciated in the context of stochastic optimal control. This study combines the Bayesian learning rule point of view into the model predictive control setting by taking inspirations from the view of understanding model predictive controller as an online learner. The selection of posterior class and natural gradient approximation for the variational formulation governs diversification of model predictive control algorithms in the Bayesian learning approach to model predictive control. This alternative viewpoint complements the dynamic mirror descent framework through streamlining the explanation of design choices.