<p>This study introduces a hybrid integral recurrent neural network (HIRNN) developed to tackle time-varying nonlinear optimization challenges characterized by multiple constraints. The proposed HIRNN architecture incorporates dynamic constraints directly into the optimization process, enabling effective performance under various types of noise, including constant, linear, and quadratic disturbances. Numerical simulations and physical experiments on a manipulator trajectory tracking task demonstrate that the proposed model achieves rapid convergence, consistent performance in the presence of disturbances, and a notable reduction in residual levels compared to existing approaches. These results highlight the enhanced accuracy and noise robustness of the HIRNN, underscoring its potential as a practical and reliable solution for time-varying constrained optimization in complex engineering applications.</p>