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    This study improves nonlinear model predictive control (MPC) by accelerating inner convex approximation. The new method enhances convergence rates for faster, more efficient real-time control applications.

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    Area of Science:

    • Control Engineering
    • Applied Mathematics

    Background:

    • Inner convex approximation enables real-time suboptimal nonlinear model predictive control (MPC).
    • Conventional methods suffer from slow convergence, limiting performance within sample times.

    Purpose of the Study:

    • To accelerate the convergence rate of inner convex approximation for suboptimal MPC.
    • To enhance the overall performance of real-time MPC systems.

    Main Methods:

    • Reformulated inner convex approximation as a nonlinear root-finding problem.
    • Performed functional analysis on the nonlinear equation (continuity, differentiability, Jacobian invertibility).
    • Applied Broyden's method to accelerate the root-finding procedure.

    Main Results:

    • Achieved a locally superlinear convergence rate for the improved algorithm.
    • Demonstrated enhanced convergence without significant additional computational cost.
    • Validated effectiveness through obstacle avoidance simulations.

    Conclusions:

    • The proposed Broyden's method-accelerated algorithm significantly improves convergence speed for inner convex approximation in MPC.
    • This advancement allows for better real-time suboptimal MPC performance and efficiency.