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    This summary is machine-generated.

    This study introduces an adaptive dynamic programming (ADP) method for multi-objective control in nonlinear systems with input interference. The approach learns Nash-optimization solutions, ensuring system stability and parameter convergence.

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    Area of Science:

    • Control Theory
    • Nonlinear Systems
    • Optimization

    Background:

    • Input-interference nonlinear systems present challenges in achieving optimal control due to competing objectives.
    • Existing methods may struggle with the complexity of multiple, individually selfish control inputs.
    • The concept of Nash equilibrium is crucial for analyzing such multi-objective scenarios.

    Purpose of the Study:

    • To develop an adaptive dynamic programming (ADP) scheme for multi-objective control in input-interference nonlinear systems.
    • To enable individual control inputs to resist weighted interference while seeking Nash-optimization solutions.
    • To achieve a defined Nash equilibrium for multiple performance indices.

    Main Methods:

    • Utilizing an adaptive neural network (NN) observer to identify system dynamics.
    • Employing critic NNs to learn multiple performance indices.
    • Designing a novel adaptive law to minimize the Hamiltonian-Jacobi-Isaacs (HJI) equation for control calculation.
    • Avoiding an actor structure by directly calculating controls from input-output data.

    Main Results:

    • The proposed ADP scheme effectively learns Nash-optimization solutions for input-interference nonlinear systems.
    • Stability of the control system and convergence of updated parameters are mathematically proven.
    • The method successfully calculates multi-objective controls using input-output data.

    Conclusions:

    • The developed ADP method provides an effective approach for multi-objective control in complex nonlinear systems.
    • The technique ensures system stability and parameter convergence, offering a robust solution.
    • Numerical simulations validate the efficacy of the proposed ADP scheme.