Closed-Loop Consistent, Causal Data-Driven Predictive Control via SSARX

TL;DR

This paper introduces a novel data-driven predictive control method using SSARX that avoids traditional Hankel matrix representations, enabling causal, noise-robust control policies directly from input-output data.

Contribution

It develops a fundamental-lemma-free, causal DDPC scheme based on SSARX, improving robustness and simplicity over existing approaches like DeePC.

Findings

Performs competitively with existing methods in noisy closed-loop scenarios

Uses high-order ARX models to decouple noise effectively

Provides a causal predictor suitable for MPC integration

Abstract

We propose a fundamental-lemma-free data-driven predictive control (DDPC) scheme for synthesizing model predictive control (MPC)-like policies directly from input-output data. Unlike the well-known DeePC approach and other DDPC methods that rely on Willems' fundamental lemma, our method avoids stacked Hankel representations and the DeePC decision variable g. Instead, we develop a closed-loop consistent, causal DDPC scheme based on the multi-step predictor Subspace-ARX (SSARX). The method first (i) estimates predictor/observer Markov parameters via a high-order ARX model to decouple the noise, then (ii) learns a multi-step past-to-future map by regression, optionally with a reduced-rank constraint. The SSARX predictor is strictly causal, which allows it to be integrated naturally into an MPC formulation. Our experimental results show that SSARX performs competitively with other methods when applied to closed-loop data affected by measurement and process noise.