A Robust Direct-Discretized RNN for Time-Dependent Optimization Constrained by Nonlinear Equalities and Its Applications

In recent years, numerous recurrent neural network (RNN) models have been reported for solving time-dependent nonlinear optimization problems. However, few existing RNN models simultaneously involve nonlinear equality constraints, direct discretization, and noise suppression. This limitation presents challenges when existing models are applied to practical engineering problems. Additionally, most current discrete-time RNN models are derived from continuous-time models, which may not perform well for solving essentially discrete problems. To handle these issues, a robust direct-discretized RNN (RDD-RNN) model is proposed to efficiently realize time-dependent optimization constrained by nonlinear equalities (TDOCNE) in the presence of various time-dependent noises. Theoretical analyses are provided to reveal that the proposed RDD-RNN model possesses excellent convergence and noise-suppressing capability. Furthermore, numerical experiments and manipulator control instances are conducted and analyzed to validate the superior robustness of the proposed RDD-RNN model under various time-dependent noises, particularly quadratic polynomial noise. Eventually, small target detection experiments further demonstrate the practicality of the RDD-RNN model in image processing applications.