Data-Driven Koopman Operator Based Cyber-Attacks for Nonlinear Control Affine Cyber-Physical Systems
Bibliographic record
Abstract
This paper studies the data-driven implementation of stealthy cyber-attacks for a class of nonlinear cyber-physical systems (CPS). In particular, we consider and study zero dynamics and covert cyber-attacks. By utilizing the Koopman operator theory, a given control affine CPS is transformed into the Koopman canonical form, and its relative degree is defined in terms of the Koopman modes, Koopman eigenvalues, and Koopman eigenfunctions. Consequently, the relative degree of the CPS is utilized to determine zero dynamics cyber-attacks. In contrast to the linear case, adversaries need to compromise both input and output communication channels of the CPS to maintain their attacks undetected. Moreover, the Koopman canonical form of the CPS is used to define and implement covert cyber-attacks in nonlinear CPS. The extended dynamic mode decomposition (EDMD) provides a linear finite-dimensional approximation of the CPS. Consequently, approximated dynamics of the CPS are utilized to introduce data-driven zero dynamics and covert cyber-attacks. Finally, a numerical example is provided to illustrate the effectiveness of our proposed methods.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".