Event-Triggered Secure Control Design Against False Data Injection Attacks via Lyapunov-Based Neural Networks
Abstract
:1. Introduction
- (i)
- Real-time hybrid anomaly detection: A hybrid detection method is developed by combining a Kalman filter with a Lyapunov-based adaptive neural network. The update laws for the neural network weights are analytically derived to ensure that the time derivative of the unified Lyapunov function remains negative definite, thereby guaranteeing the stability of both the closed-loop system and the neural network dynamics.
- (ii)
- Resource-aware secure control: A composite control structure is designed by integrating the hybrid observer with a state-dependent event-triggered mechanism. The triggering condition is dynamically adjusted based on the estimation feedback, allowing control updates to occur only when necessary. This strategy enhances resilience while significantly reducing communication and computational overhead.
- (iii)
- Stability-guaranteed LMI-based threshold synthesis: A unified Lyapunov function is constructed to capture both estimation and triggering dynamics. Based on this formulation, LMI conditions are derived to ensure boundedness of estimation and system errors. The triggering threshold is treated as a decision variable within the LMI framework, enabling systematic optimization for both stability assurance and resource efficiency.
2. Mathematical Model
2.1. FDI Attacks Model
2.2. System Model Under FDI Attack
3. Event-Triggered Control
4. Attack Detection
4.1. Observer Design
4.2. Neural Network
5. Stability Analysis
6. Simulation Results
- Case 1: Abrupt Attack. Abrupt attacks involve sudden, step-like deviations that cause immediate disruption in system behavior. In this scenario, a constant bias is injected into the second state from the beginning of the simulation. The injected signal is defined as follows
- Case 2: Incipient Attack. Incipient attacks evolve slowly over time, often staying below detection thresholds and mimicking benign signal variations. The injected bias is modeled as the step response of a first-order system
- Case 3: Triangle Attack. Triangle attacks feature a linearly increasing injection followed by a linear decay, bridging the behavioral characteristics between abrupt and incipient faults. The injected signal is defined as
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
2-DOF | Two-degree-of-freedom |
CBFs | Control barrier functions |
DoS | Denial of service |
ETC | Event-triggered control |
FDI | False data injection |
HRI | Human–robot interaction |
ISE | Integral square error |
LMI | Linear matrix inequality |
LQR | Linear quadratic regulator |
NN | Neural network |
RMSE | Root mean square error |
UUB | Uniform ultimate bounded |
ZOH | Zero-order hold |
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Attack Type | RMSE |
---|---|
Case 1: Abrupt | |
Case 2: Incipient | |
Case 3: Triangle |
Controller | Scenario | ISE |
---|---|---|
Case 1: Abrupt | 0.2436 | |
Classical LQR | Case 2: Incipient | 0.2398 |
Case 3: Triangle | 70.17 | |
Case 1: Abrupt | 0.02497 | |
Proposed Method | Case 2: Incipient | 0.005807 |
Case 3: Triangle | 0.02823 |
Controller | Case | ||
---|---|---|---|
Case 1: Abrupt | 1.776 | 235.8 | |
Classical LQR | Case 2: Incipient | 1.938 | 284.9 |
Case 3: Triangle | 472.6 | 94,040 | |
Case 1: Abrupt | 0.6134 | 25.2 | |
Proposed Method | Case 2: Incipient | 0.489 | 21.79 |
Case 3: Triangle | 6.258 | 503.2 |
Control Strategy | Case | Number of Transmissions |
---|---|---|
Case 1: Abrupt | 15,000 | |
Time-Triggered Control | Case 2: Incipient | 20,000 |
Case 3: Triangle | 50,000 | |
Case 1: Abrupt | 407 | |
Event-Triggered Control | Case 2: Incipient | 515 |
Case 3: Triangle | 1416 |
Control Strategy | Case | Time |
---|---|---|
Case 1: Abrupt | 0.04032 | |
Time-Triggered Control | Case 2: Incipient | 0.05187 |
Case 3: Triangle | 0.1352 | |
Case 1: Abrupt | 0.001406 | |
Event-Triggered Control | Case 2: Incipient | 0.001813 |
Case 3: Triangle | 0.005149 |
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Kutlucan, N.K.; Ucun, L.; Dasdemir, J. Event-Triggered Secure Control Design Against False Data Injection Attacks via Lyapunov-Based Neural Networks. Sensors 2025, 25, 3634. https://doi.org/10.3390/s25123634
Kutlucan NK, Ucun L, Dasdemir J. Event-Triggered Secure Control Design Against False Data Injection Attacks via Lyapunov-Based Neural Networks. Sensors. 2025; 25(12):3634. https://doi.org/10.3390/s25123634
Chicago/Turabian StyleKutlucan, Neslihan Karas, Levent Ucun, and Janset Dasdemir. 2025. "Event-Triggered Secure Control Design Against False Data Injection Attacks via Lyapunov-Based Neural Networks" Sensors 25, no. 12: 3634. https://doi.org/10.3390/s25123634
APA StyleKutlucan, N. K., Ucun, L., & Dasdemir, J. (2025). Event-Triggered Secure Control Design Against False Data Injection Attacks via Lyapunov-Based Neural Networks. Sensors, 25(12), 3634. https://doi.org/10.3390/s25123634