Multirate Data-Driven Predictive Control: Rank Obstructions, Identifiability, and Noise Conditioning
Abstract
We develop rank, identifiability, and noise-conditioning results for compact input--output predictors in multirate data-driven predictive control. The inverse of a square zero-input response matrix used in an existing compact-lifting construction is shown to be undefined under its observability and minimal-polynomial assumptions. We derive exact replacements using rank-complete data, characterize all predictor extensions, and establish the minimum-norm and minimax Euclidean noise properties of the canonical Moore--Penrose extension. A joint predictor is identified directly from mixed experiments with arbitrary initial states. Deterministic perturbation bounds quantify reconstruction errors through informative singular-value margins, while a positive-definite reduced weighting preserves the nominal quadratic cost. Sampling-rate observability and event-triggering analyses identify additional conditions needed for reconstruction and stability guarantees.
Related
- A Robust Control Architecture for Multirate Systems and their Interconnections
- Data-Driven Stochastic Control of Delayed Air-Conditioning Systems
- A Multirate Transient Simulation Technique for Circuits described by Integro-Differential Equations
- Model Predictive Control: Systematic Design Tailored to Nonholonomic Systems
- SD-DPC: Sparse Dictionary Differentiable Predictive Control
BibTeX
@misc{vrabel2026multirate,
title = {{Multirate Data-Driven Predictive Control: Rank Obstructions, Identifiability, and Noise Conditioning}},
author = {Robert Vrabel},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01665},
eprint = {2611.01665},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01665},
}
RIS
TY - UNPB
TI - Multirate Data-Driven Predictive Control: Rank Obstructions, Identifiability, and Noise Conditioning
AU - Robert Vrabel
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01665
UR - https://arxiv.org/abs/2611.01665
AB - We develop rank, identifiability, and noise-conditioning results for compact input--output predictors in multirate data-driven predictive control. The inverse of a square zero-input response matrix used in an existing compact-lifting construction is shown to be undefined under its observability and minimal-polynomial assumptions. We derive exact replacements using rank-complete data, characterize all predictor extensions, and establish the minimum-norm and minimax Euclidean noise properties of the canonical Moore--Penrose extension. A joint predictor is identified directly from mixed experiments with arbitrary initial states. Deterministic perturbation bounds quantify reconstruction errors through informative singular-value margins, while a positive-definite reduced weighting preserves the nominal quadratic cost. Sampling-rate observability and event-triggering analyses identify additional conditions needed for reconstruction and stability guarantees.
ER -