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    A new distributed policy iteration algorithm improves control laws iteratively for nonlinear systems, reducing computational load. This method ensures convergence to optimal control solutions for infinite horizon problems.

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    Area of Science:

    • Control Theory
    • Nonlinear Systems
    • Optimization

    Background:

    • Infinite horizon optimal control problems are crucial for continuous-time nonlinear systems.
    • Traditional policy iteration algorithms can be computationally intensive due to simultaneous updates.

    Purpose of the Study:

    • To establish a novel distributed policy iteration algorithm for continuous-time nonlinear systems.
    • To reduce the computational burden in each iteration compared to traditional methods.

    Main Methods:

    • A distributed policy iteration algorithm where only one controller's law is updated per iteration.
    • Analysis of algorithm properties including admissibility, monotonicity, and convergence.
    • Numerical simulations to validate the proposed method.

    Main Results:

    • The iterative value function is shown to be nonincreasingly convergent.
    • The algorithm converges to the solution of the Hamilton-Jacobi-Bellman equation.
    • Effectiveness demonstrated through numerical simulations.

    Conclusions:

    • The proposed distributed policy iteration algorithm effectively solves infinite horizon optimal control problems for continuous-time nonlinear systems.
    • The iterative, one-by-one update strategy significantly reduces computational complexity.
    • The method guarantees convergence and optimality, validated by theoretical analysis and simulations.