A High Order Integration Enhanced Zeroing Neural Network for Time-Varying Convex Quadratic Program Against Nonlinear Noise

The quadratic programming (QP) problem constitutes a distinctive class within mathematical optimization, prevalent in scientific computations and engineering applications. In practical scenarios, noise interference has the potential to adversely impact the solution accuracy of time-varying QP (TVQP) problems, thereby compromising the performance of established neural network models, including the original zeroing neural network (OZNN). Consequently, certain variants of the Zeroing Neural Network (ZNN) model exhibit notable tolerance to constant or linear noise; however, it is imperative to acknowledge the prevalence of more intricate forms of noise, particularly nonlinear noise. To ameliorate compromised solution accuracy in the presence of nonlinear noise, this study introduces a novel Zeroing Neural Network (ZNN) model, denoted as Triple Integral Enhancement Zeroing Neural Network (TIEZNN). The model incorporates a novel error processing mechanism strategically enhanced through triple integral augmentation, designed specifically to address TVQP perturbed by nonlinear noise. Theoretical analysis rigorously establishes the convergence properties and commendable noise suppression capabilities intrinsic to the proposed TIEZNN model. Compared with the traditional gradient-based neural network and the previous ZNN model and its variants, the TIEZNN model proposed in this paper is still highly robust and accurate in the face of nonlinear noise. Simulation results unequivocally demonstrate the efficiency and superior performance of the TIEZNN model in addressing TVQP challenges, particularly in scenarios featuring equality and inequality constraints influenced by nonlinear noise.