Advanced Observation-Based Bipartite Containment Control of Fractional-Order Multi-Agent Systems Considering Hostile Environments, Nonlinear Delayed Dynamics, and Disturbance Compensation
Abstract
1. Introduction
- As compared to [29], we use a fractional-order multi-agent system instead of an integer-order derivative; our work contributes to the field by providing a more general and flexible framework for modeling and controlling dynamic behaviors in complex networks.
- By incorporating disturbances into the controller, our work enhances the robustness and practical applicability of the control strategy for fractional-order multi-agent systems, addressing real-world uncertainties.
- By incorporating a nonlinear delayed function in the dynamics, our work provides a more accurate and comprehensive framework for modeling and controlling fractional-order multi-agent systems, capturing complex temporal interactions and delays that have not been addressed in previous studies [29].
- 1.
- Section 1 is the introduction of the paper.
- 2.
- Section 2 presents the foundational knowledge that is useful for our main results.
- 3.
- Observation-based analyses of bipartite containment control for fixed and switching signed digraphs are discussed in Section 3.2 and Section 4.
- 4.
- Numerical examples are presented in Section 5.
- 5.
- The paper is summarized in Section 6.
2. Foundational Knowledge
2.1. Graph Theory
2.2. Basic Lemmas and Fractional Operators
3. Observation-Based Bipartite Containment Control Analysis
3.1. Model Building
3.2. Observation-Based Analysis of Bipartite Multi-Agent System for Fixed Signed Digraph
- , where:
- -
- -
- , where:
- -
- -
4. Observation-Based Analysis of Bipartite Containment Control for Switching Signed Digraph
- , where:
- -
- -
- , where:
- -
- -
5. Numerical Illustrations
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Khan, A.; Javeed, M.A.; Rehman, S.; Niazi, A.U.K.; Zhong, Y. Advanced Observation-Based Bipartite Containment Control of Fractional-Order Multi-Agent Systems Considering Hostile Environments, Nonlinear Delayed Dynamics, and Disturbance Compensation. Fractal Fract. 2024, 8, 473. https://doi.org/10.3390/fractalfract8080473
Khan A, Javeed MA, Rehman S, Niazi AUK, Zhong Y. Advanced Observation-Based Bipartite Containment Control of Fractional-Order Multi-Agent Systems Considering Hostile Environments, Nonlinear Delayed Dynamics, and Disturbance Compensation. Fractal and Fractional. 2024; 8(8):473. https://doi.org/10.3390/fractalfract8080473
Chicago/Turabian StyleKhan, Asad, Muhammad Awais Javeed, Saadia Rehman, Azmat Ullah Khan Niazi, and Yubin Zhong. 2024. "Advanced Observation-Based Bipartite Containment Control of Fractional-Order Multi-Agent Systems Considering Hostile Environments, Nonlinear Delayed Dynamics, and Disturbance Compensation" Fractal and Fractional 8, no. 8: 473. https://doi.org/10.3390/fractalfract8080473
APA StyleKhan, A., Javeed, M. A., Rehman, S., Niazi, A. U. K., & Zhong, Y. (2024). Advanced Observation-Based Bipartite Containment Control of Fractional-Order Multi-Agent Systems Considering Hostile Environments, Nonlinear Delayed Dynamics, and Disturbance Compensation. Fractal and Fractional, 8(8), 473. https://doi.org/10.3390/fractalfract8080473