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    A novel neural controller effectively tracks trajectories in uncertain complex networks by pinning a fraction of nodes. This method ensures stability and demonstrates high performance in chaotic systems.

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    Area of Science:

    • Complex Networks
    • Control Theory
    • Neural Networks

    Background:

    • Trajectory tracking in uncertain complex networks presents significant challenges.
    • Existing control methods may struggle with the inherent complexity and uncertainty of these systems.
    • The need for robust and efficient control strategies is paramount for network stability and performance.

    Purpose of the Study:

    • To propose a new control approach for trajectory tracking in uncertain complex networks.
    • To implement a neural controller on a subset of network nodes (pinned nodes).
    • To ensure and analyze the stability of the proposed control scheme.

    Main Methods:

    • A neural controller is designed, comprising an on-line identifier utilizing a recurrent high-order neural network.
    • An inverse optimal controller is integrated for precise trajectory tracking.
    • A stability analysis is performed to validate the control scheme's robustness.

    Main Results:

    • The proposed neural controller successfully achieves trajectory tracking on uncertain complex networks.
    • Simulations using a network of chaotic Lorenz oscillators demonstrate the control scheme's applicability and effectiveness.
    • The pinning strategy on a fraction of nodes proves efficient for controlling the entire network's dynamics.

    Conclusions:

    • The developed neural control approach offers a viable solution for trajectory tracking in complex, uncertain network environments.
    • The combination of on-line identification and inverse optimal control ensures reliable performance.
    • The study validates the effectiveness of controlling complex networks via targeted node manipulation.