A Game-Theoretic Framework for Security-Aware Sensor Placement Problem in Networked Control Systems
Bibliographic record
Abstract
This article studies the sensor placement problem in a leader–follower networked control system for improving its security against cyber-physical attacks. In a zero-sum game, the attacker selects$f$nodes of the network to attack, and the detector places$f$sensors to detect the presence of the attack signals. In our formulation, the attacker’s objective is to have a large impact on a target node in the network while being as little visible as possible to the detector. The detector, however, seeks to maximize the visibility of the attack signals. The effects of the attack signals on both the target node and the detector node are captured via the system$L_2$gain from the attack signals to the target node and deployed sensors’ outputs, respectively. The equilibrium strategy of the game determines the optimal locations of the sensors. The existence of Nash equilibrium for the single-attack single-sensor case is studied when the underlying connectivity graph is a directed or an undirected tree. We show that, under the optimal sensor placement strategy, an undirected topology provides a higher security level for a networked control system compared to its corresponding directed topology. For the multiple-attack multiple-sensor case, we show that the game does not necessarily admit a Nash equilibrium and introduce a Stackelberg game approach, where the detector acts as the leader. Finally, these results are used to study the sensor placement problem in a vehicle platooning application in the presence of bias injectionattacks.
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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 | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".