Harnessing Uncertainty for a Separation Principle in Direct Data-Driven Predictive Control

TL;DR

This paper introduces a stochastic framework for direct data-driven predictive control that incorporates uncertainty, establishing a separation principle and improving robustness and optimality over existing methods.

Contribution

It presents a unified approach to direct DDPC with a separation principle, generalizing existing methods and providing noise-tolerance with theoretical guarantees.

Findings

The proposed method outperforms existing DDPC techniques in experiments.

It automatically accounts for uncertainty without tuning regularization parameters.

The framework generalizes regularized DeePC and γ-DDPC methods.

Abstract

Model Predictive Control (MPC) is a powerful method for complex system regulation, but its reliance on an accurate model poses many limitations in real-world applications. Data-driven predictive control (DDPC) aims at overcoming this limitation, by relying on historical data to provide information on the plant to be controlled. In this work, we present a unified stochastic framework for direct DDPC, where control actions are obtained by optimizing the Final Control Error (FCE), which is directly computed from available data only and automatically weighs the impact of uncertainty on the control objective. Our framework allows us to establish a separation principle for Predictive Control, elucidating the role that predictive models and their uncertainty play in DDPC. Moreover, it generalizes existing DDPC methods, like regularized Data-enabled Predictive Control (DeePC) and $\gamma$-DDPC, providing a path toward noise-tolerant data-based control with rigorous optimality guarantees. The theoretical investigation is complemented by a series of experiments (code available on GitHub: https://github.com/marcofabris92/a-separation-principle-in-d3pc), revealing that the proposed method consistently outperforms or, at worst, matches existing techniques without requiring tuning regularization parameters as other methods do.