Stochastic Data-Driven Predictive Control: Regularization, Estimation, and Constraint Tightening

TL;DR

This paper advances stochastic data-driven predictive control by introducing regularization, initial condition estimation, and constraint tightening techniques to handle uncertainties, improving control performance and reliability.

Contribution

It proposes a tuning-free regularizer, a stochastic initial condition estimator, and a second-order cone-based constraint tightening method for robust data-driven control.

Findings

Enhanced control performance with reduced control cost

Improved initial condition estimation accuracy

High-probability constraint satisfaction achieved

Abstract

Data-driven predictive control methods based on the Willems' fundamental lemma have shown great success in recent years. These approaches use receding horizon predictive control with nonparametric data-driven predictors instead of model-based predictors. This study addresses three problems of applying such algorithms under unbounded stochastic uncertainties: 1) tuning-free regularizer design, 2) initial condition estimation, and 3) reliable constraint satisfaction, by using stochastic prediction error quantification. The regularizer is designed by leveraging the expected output cost. An initial condition estimator is proposed by filtering the measurements with the one-step-ahead stochastic data-driven prediction. A novel constraint-tightening method, using second-order cone constraints, is presented to ensure high-probability chance constraint satisfaction. Numerical results demonstrate that the proposed methods lead to satisfactory control performance in terms of both control cost and constraint satisfaction, with significantly improved initial condition estimation.