The Bayesian Separation Principle for Data-driven Control

TL;DR

This paper demonstrates a Bayesian separation principle in data-driven control, showing it holds universally and can improve control performance by incorporating uncertainty, with applications to linear and nonlinear systems.

Contribution

It introduces a Bayesian separation principle for model predictive control that is valid regardless of data size, enabling uncertainty-aware control design.

Findings

Bayesian separation principle holds universally, regardless of data size.

Incorporating uncertainty improves control performance over nominal methods.

Numerical results show advantages in linear and nonlinear scenarios.

Abstract

In this paper we investigate the existence of a separation principle between model identification and control design in the context of model predictive control. First, we clarify that such a separation principle holds asymptotically in the number of data in a Fisherian context, and show that it holds universally, i.e. regardless of the data size, in a Bayesian context. Then, by formulating model predictive control within a Gaussian regression framework, we describe how the Bayesian separation principle can be used to derive computable, uncertainty-aware expressions for the control cost and optimal input sequence, thereby bridging direct and indirect data-driven approaches. Numerical results in both linear and nonlinear scenarios illustrate that the proposed approach outperform nominal methods that neglect uncertainty, highlighting the advantages of incorporating uncertainty in the control design process.