A Stochastic Fundamental Lemma with Reduced Disturbance Data Requirements
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909008593420288 |
|---|---|
| author | Ou, Ruchuan Pan, Guanru Faulwasser, Timm |
| author_facet | Ou, Ruchuan Pan, Guanru Faulwasser, Timm |
| contents | Recently, the fundamental lemma by Willems et al. has been extended towards stochastic LTI systems subject to process disturbances. Using this lemma requires previously recorded data of inputs, outputs, and disturbances. In this paper, we exploit causality concepts of stochastic control to propose a variant of the stochastic fundamental lemma that does not require past disturbance data in the Hankel matrices. Our developments rely on polynomial chaos expansions and on the knowledge of the disturbance distribution. Similar to our previous results, the proposed variant of the fundamental lemma allows to predict future input-output trajectories of stochastic LTI systems. We draw upon a numerical example to illustrate the proposed variant in data-driven control context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09131 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Stochastic Fundamental Lemma with Reduced Disturbance Data Requirements Ou, Ruchuan Pan, Guanru Faulwasser, Timm Systems and Control Optimization and Control Recently, the fundamental lemma by Willems et al. has been extended towards stochastic LTI systems subject to process disturbances. Using this lemma requires previously recorded data of inputs, outputs, and disturbances. In this paper, we exploit causality concepts of stochastic control to propose a variant of the stochastic fundamental lemma that does not require past disturbance data in the Hankel matrices. Our developments rely on polynomial chaos expansions and on the knowledge of the disturbance distribution. Similar to our previous results, the proposed variant of the fundamental lemma allows to predict future input-output trajectories of stochastic LTI systems. We draw upon a numerical example to illustrate the proposed variant in data-driven control context. |
| title | A Stochastic Fundamental Lemma with Reduced Disturbance Data Requirements |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2502.09131 |