The Bias of Subspace-based Data-Driven Predictive Control
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908431765471232 |
|---|---|
| author | Moffat, Keith Dörfler, Florian Chiuso, Alessandro |
| author_facet | Moffat, Keith Dörfler, Florian Chiuso, Alessandro |
| contents | This paper quantifies and addresses the bias of subspace-based Data-Driven Predictive Control (DDPC) for linear, time-invariant (LTI) systems. The primary focus is the bias that arises when the training data is gathered with a feedback controller in closed-loop with the system. First, the closed-loop bias of Subspace Predictive Control is quantified using the training data innovations. Next, the bias of direct, subspace-based DDPC methods DeePC and $γ$-DDPC is shown to consist of two parts--the Subspace Bias, which arises from closed-loop data, and an Optimism Bias, which arises from DeePC/$γ$-DDPC's "optimistic" adjustment of the output trajectory. We show that, unlike subspace-based DDPC methods, Transient Predictive Control does not suffer from Subspace Bias or Optimism Bias. Double integrator experiments demonstrate that Subspace and Optimism Bias are responsible for poor reference tracking by the subspace-based DDPC methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02468 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Bias of Subspace-based Data-Driven Predictive Control Moffat, Keith Dörfler, Florian Chiuso, Alessandro Systems and Control This paper quantifies and addresses the bias of subspace-based Data-Driven Predictive Control (DDPC) for linear, time-invariant (LTI) systems. The primary focus is the bias that arises when the training data is gathered with a feedback controller in closed-loop with the system. First, the closed-loop bias of Subspace Predictive Control is quantified using the training data innovations. Next, the bias of direct, subspace-based DDPC methods DeePC and $γ$-DDPC is shown to consist of two parts--the Subspace Bias, which arises from closed-loop data, and an Optimism Bias, which arises from DeePC/$γ$-DDPC's "optimistic" adjustment of the output trajectory. We show that, unlike subspace-based DDPC methods, Transient Predictive Control does not suffer from Subspace Bias or Optimism Bias. Double integrator experiments demonstrate that Subspace and Optimism Bias are responsible for poor reference tracking by the subspace-based DDPC methods. |
| title | The Bias of Subspace-based Data-Driven Predictive Control |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2507.02468 |