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    Area of Science:

    • Network Science
    • Control Theory
    • Dynamical Systems

    Background:

    • Real-world networked systems exhibit time-varying connectivity, leading to complex dynamics.
    • Existing control frameworks are primarily designed for static networks, lacking methods for temporal networks.
    • Controlling temporal networks is challenging, especially when input and source-node connections are variable.

    Purpose of the Study:

    • To develop novel control strategies for temporal networks.
    • To reduce control effort and energy consumption in time-varying systems.
    • To address the limitations of static network control frameworks.

    Main Methods:

    • Formulation of a quadratic energy cost function, avoiding the Riccati differential equation.
    • Development of methods to improve system trajectories and input matrices for reduced control effort.
    • Integration of coordinate descent, linearly constrained quadratic programming, and projected gradient descent algorithms.

    Main Results:

    • Demonstrated substantial reduction in control effort by optimizing system trajectories and input matrices.
    • Showcased the potential of temporal networks as energy-efficient control systems.
    • Presented effective strategies for improving control input in dynamic networks.

    Conclusions:

    • The proposed methods offer a new approach to controlling temporal networks efficiently.
    • The algorithms provide a foundation for engineering real-world temporal networks.
    • This work highlights the energy-saving potential of dynamic network control.