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    This study introduces a simultaneous policy iteration (SPI) algorithm for uncertain nonlinear systems. The method effectively solves constrained optimization problems using approximate dynamic programming and actor-critic networks.

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    Area of Science:

    • Control Theory
    • Optimization
    • Artificial Intelligence

    Background:

    • Constrained optimization problems in uncertain nonlinear interconnected systems are complex.
    • Existing methods may struggle with the inherent uncertainties and interconnections.
    • Approximate dynamic programming offers a potential framework for such problems.

    Purpose of the Study:

    • To develop a novel algorithm for solving constrained optimization problems in uncertain nonlinear interconnected systems.
    • To demonstrate the convergence and effectiveness of the proposed algorithm.
    • To implement the algorithm using an actor-critic structure for practical application.

    Main Methods:

    • Proving that the constrained optimization solution can be derived from auxiliary subsystems.
    • Presenting a simultaneous policy iteration (SPI) algorithm within approximate dynamic programming.
    • Implementing SPI using actor-critic networks for policy approximation and value function estimation.
    • Utilizing least squares and Monte Carlo integration for network weight determination.

    Main Results:

    • The equivalence between the original problem and auxiliary subsystems is established.
    • The convergence of the simultaneous policy iteration (SPI) algorithm is demonstrated.
    • The actor-critic implementation effectively approximates optimal control policies and value functions.
    • Simulations confirm the efficacy of the developed control method on a nonlinear interconnected plant.

    Conclusions:

    • The simultaneous policy iteration (SPI) algorithm provides an effective solution for constrained optimization in uncertain nonlinear interconnected systems.
    • The actor-critic implementation offers a practical approach for real-world applications.
    • The study validates the developed control method through simulation, highlighting its potential.