Fuzzy Adaptive Approaches for Robust Containment Control in Nonlinear Multi-Agent Systems under False Data Injection Attacks
Abstract
:1. Introduction
- The development of a novel fuzzy adaptive control strategy specifically designed for nonlinear multi-agent systems under FDI attacks
- A detailed stability analysis that validates the effectiveness of the proposed method
- Extensive simulations that compare our method with existing approaches show significant improvements in both adaptability and robustness.
- We introduce our work in Section 1.
- In Section 2, graph theory is explained for the communication of agents. Some lemmas and definitions are provided.
- Section 3 provides a system model that explains the dynamic of leaders and followers.
- In Section 4, main results are presented.
- Section 5 provides a numerical experiment, and two examples are provided for the effectiveness of the results.
- In Section 6, we draw conclusions.
2. Preliminaries
2.1. Definition and Lemmas
2.2. Introduction to Interval Type-II Fuzzy Systems
3. System Model
- denotes the fractional derivative of order ,
- is the state vector of the p-th follower,
- represents the nonlinear dynamics of the system,
- is the saturated control input,
- denotes false data injected by the adversary.
- Leader Dynamics: In the diagram, the leader dynamics are represented as the driving force of the system. The leader agents provide the desired trajectories or reference signals that guide the follower agents. These trajectories represent the target behaviors that the followers aim to achieve. The leader dynamics set the objectives for the system, which are tracked by the followers through feedback control mechanisms.
- Follower Dynamics: The follower agents are represented in the block diagram as systems that track the leaders’ behavior. Each follower adjusts its state based on both its local interactions and the leader’s state. The dynamics of these followers are influenced by the control inputs received from the fuzzy controller. Followers work together to reach the leaders’ trajectories while maintaining a desired formation or coordinated behavior.
- Fuzzy Controller: The fuzzy controller is shown as the primary decision-making block that processes input information from both the leaders and followers. It maps the input errors (the difference between the leader and follower states) to appropriate control actions using fuzzy logic rules. The fuzzy controller helps manage uncertainties and nonlinearities in the system by generating adaptive control signals that adjust the behavior of the followers.
- Adaptive Laws: The adaptive laws are depicted as a mechanism that adjusts the parameters of the fuzzy controller over time. They allow the system to adapt to unknown or changing dynamics within the leader–follower interactions, ensuring robustness against disturbances or modeling inaccuracies. Adaptive laws ensure that the control gains are modified continuously based on system performance, allowing the system to remain stable and achieve the desired tracking performance.
3.1. Attack Model
3.1.1. Nature of FDI Attacks
3.1.2. Mechanisms of Injection
3.2. Impact on System Dynamics
- is the state vector of the k-th leader,
- represents the dynamics of the leader.
- , , , ,
- , , , , .
- The set of values represents the adjacent neighbors of agents .
- The position is guided to converge towards the convex hull defined by the positions of the leader agents. This convergence is expressed by:
- The controller of each follower agent p is constrained to remain within a specified range, . Here, and are predetermined constants, with being negative and being positive.
4. Main Results
5. Numerical Illustration
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Alsinai, A.; Al-Shamiri, M.M.A.; Ul Hassan, W.; Rehman, S.; Niazi, A.U.K. Fuzzy Adaptive Approaches for Robust Containment Control in Nonlinear Multi-Agent Systems under False Data Injection Attacks. Fractal Fract. 2024, 8, 506. https://doi.org/10.3390/fractalfract8090506
Alsinai A, Al-Shamiri MMA, Ul Hassan W, Rehman S, Niazi AUK. Fuzzy Adaptive Approaches for Robust Containment Control in Nonlinear Multi-Agent Systems under False Data Injection Attacks. Fractal and Fractional. 2024; 8(9):506. https://doi.org/10.3390/fractalfract8090506
Chicago/Turabian StyleAlsinai, Ammar, Mohammed M. Ali Al-Shamiri, Waqar Ul Hassan, Saadia Rehman, and Azmat Ullah Khan Niazi. 2024. "Fuzzy Adaptive Approaches for Robust Containment Control in Nonlinear Multi-Agent Systems under False Data Injection Attacks" Fractal and Fractional 8, no. 9: 506. https://doi.org/10.3390/fractalfract8090506