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    Area of Science:

    • Robotics and Control Systems
    • Artificial Intelligence
    • System Dynamics

    Background:

    • Classical optimal bounded ellipsoid (OBE) algorithms face challenges with unbounded learning gain matrices.
    • Uncertainty in Euler-Lagrange systems necessitates robust identification methods.
    • Existing OBE algorithms lack deterministic bounds for learning gain matrices, impacting performance.

    Purpose of the Study:

    • To propose an effective optimal bounded ellipsoid (OBE) identification algorithm for neural networks.
    • To reconstruct the dynamics of uncertain Euler-Lagrange systems.
    • To ensure deterministic upper and lower bounds for the learning gain matrix, independent of excitation levels.

    Main Methods:

    • Development of a modified OBE algorithm with predetermined bounds for the learning gain matrix.
    • Application of the OBE algorithm for neural network-based system identification.
    • Design of a closed-loop controller for Euler-Lagrange systems using the proposed identification algorithm.
    • Lyapunov stability theory for proving practical asymptotic stability.

    Main Results:

    • The modified OBE algorithm guarantees deterministic upper and lower bounds for the learning gain matrix.
    • The proposed controller ensures practical asymptotic stability for the closed-loop system.
    • The controller does not require inertial matrix inversion or noisy acceleration signals.
    • Comparative studies validate the effectiveness of the proposed approach.

    Conclusions:

    • The novel OBE identification algorithm effectively reconstructs Euler-Lagrange system dynamics.
    • The bounded learning gain matrix improves robustness and performance.
    • The developed controller offers a practical and stable solution for Euler-Lagrange systems without complex computations.