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    This study introduces a novel control scheme for complex multi-input multi-output (MIMO) systems, ensuring practical time-synchronized tracking control despite system challenges. The new method achieves synchronous convergence of tracking errors efficiently.

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    Area of Science:

    • Control Systems Engineering
    • Nonlinear System Dynamics
    • Robotics and Automation

    Background:

    • Existing control methods struggle with time-synchronized tracking in multi-input multi-output (MIMO) systems, particularly those with unmatched nonlinearities and input saturations.
    • The 'explosion of complexity' and filtering errors are significant challenges in high-order nonlinear system control.
    • Input saturation limits the performance and stability of control systems.

    Purpose of the Study:

    • To develop a practically time-synchronized control scheme for MIMO systems with unmatched nonlinearities and input saturations.
    • To address and mitigate the 'explosion of complexity' and filtering error issues.
    • To ensure all tracking error components converge synchronously to a small neighborhood of the origin in finite time.

    Main Methods:

    • A practically time-synchronized command filtered backstepping (CFB) control scheme is proposed.
    • Integration of modified command filters and norm-normalized sign functions for control signal design.
    • Recursive embedding of novel auxiliary systems to counteract input saturation effects.

    Main Results:

    • The proposed CFB framework guarantees practical time-synchronized convergence.
    • Simultaneous resolution of 'explosion of complexity' and filtering errors.
    • All tracking error components achieve finite-time synchronous convergence despite system complexities.

    Conclusions:

    • The novel time-synchronized CFB control scheme effectively handles unmatched nonlinearities and input saturations in MIMO systems.
    • The method demonstrates superior performance in achieving practical synchronous convergence compared to existing approaches.
    • Theoretical analysis and simulations validate the proposed control scheme's effectiveness and superiority.