On the Sharp Input-Output Analysis of Nonlinear Systems under Adversarial Attacks
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908558832959488 |
|---|---|
| author | Kim, Jihun Fang, Yuchen Lavaei, Javad |
| author_facet | Kim, Jihun Fang, Yuchen Lavaei, Javad |
| contents | This paper is concerned with learning the input-output mapping of general nonlinear dynamical systems. While the existing literature focuses on Gaussian inputs and benign disturbances, we significantly broaden the scope of admissible control inputs and allow correlated, nonzero-mean, adversarial disturbances. With our reformulation as a linear combination of basis functions, we prove that the $\ell_2$-norm estimator overcomes the challenges as long as the probability that the system is under adversarial attack at a given time is smaller than a certain threshold. We provide an estimation error bound that decays with the input memory length and prove its optimality by constructing a problem instance that suffers from the same bound under adversarial attacks. Our work provides a sharp input-output analysis for a generic nonlinear and partially observed system under significantly generalized assumptions compared to existing works. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11688 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Sharp Input-Output Analysis of Nonlinear Systems under Adversarial Attacks Kim, Jihun Fang, Yuchen Lavaei, Javad Optimization and Control Systems and Control 93B15, 93B30, 93C10 This paper is concerned with learning the input-output mapping of general nonlinear dynamical systems. While the existing literature focuses on Gaussian inputs and benign disturbances, we significantly broaden the scope of admissible control inputs and allow correlated, nonzero-mean, adversarial disturbances. With our reformulation as a linear combination of basis functions, we prove that the $\ell_2$-norm estimator overcomes the challenges as long as the probability that the system is under adversarial attack at a given time is smaller than a certain threshold. We provide an estimation error bound that decays with the input memory length and prove its optimality by constructing a problem instance that suffers from the same bound under adversarial attacks. Our work provides a sharp input-output analysis for a generic nonlinear and partially observed system under significantly generalized assumptions compared to existing works. |
| title | On the Sharp Input-Output Analysis of Nonlinear Systems under Adversarial Attacks |
| topic | Optimization and Control Systems and Control 93B15, 93B30, 93C10 |
| url | https://arxiv.org/abs/2505.11688 |