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    This study introduces a distributed model-predictive control (DMPC) strategy for linear systems with coupled constraints. It uses a novel primal-dual algorithm for efficient computation and guarantees system stability and feasibility.

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    Area of Science:

    • Control Systems Engineering
    • Optimization Theory
    • Distributed Computing

    Background:

    • Model-predictive control (MPC) is crucial for complex systems but computationally intensive.
    • Distributed MPC (DMPC) offers scalability but faces challenges with coupled constraints.
    • Efficient algorithms are needed to handle the computational burden of DMPC.

    Purpose of the Study:

    • To develop a computationally efficient DMPC strategy for discrete-time linear systems with globally coupled constraints.
    • To enable early termination of distributed optimization algorithms through constraint tightening.
    • To ensure recursive feasibility and closed-loop stability despite inexact solutions.

    Main Methods:

    • Constraint tightening technique for early algorithm termination.
    • Lagrangian method to convert constrained to unconstrained saddle-point problems.
    • Primal-dual algorithm utilizing Laplacian consensus for distributed dual variable estimation.

    Main Results:

    • Theoretical proof of geometric convergence for the primal-dual gradient optimization algorithm using contraction theory.
    • Derivation of an exact convergence rate, bounding the number of iterations.
    • Demonstration of recursive feasibility and closed-loop stability with inexact solutions.

    Conclusions:

    • The proposed DMPC strategy effectively addresses globally coupled constraints in discrete-time linear systems.
    • The novel primal-dual algorithm ensures computational efficiency and theoretical convergence guarantees.
    • Numerical simulations validate the performance and practical applicability of the DMPC strategy.