A universal noise-suppressing neural algorithm framework aided with nonconvex activation function for time-varying quadratic programming problems

Abstract

Time-varying quadratic programming problems (TVQPPs) subject to equality and inequality constraints with different measurement noises often arise in the fields of scientific and economic research. Noises are always ubiquitous and unavoidable in practical problems. However, most existing methods usually assume that the computing process is free of measurement noise or the denoising has been monitored before the calculation. The zeroing neural network (ZNN), a significant neurodynamic approach, has presented potent abilities to compute a great variety of time-varying zeroing problems with odd monotonically increasing activation functions, but the existing results on ZNN cannot deal with the inequality constraints in the TVQPPs. In this article, a nonconvex function activated implicit ZNN (NIZNN) model and a noise-suppressing implicit ZNN (NNSIZNN) model, which is also known as the ZNN-based model, are proposed by the inspiration of the conventional ZNN model from a control-based framework. It guarantees an effective solution for TVQPPs in the presence of different noises. The ZNN-based model allows nonconvex sets for projection operation in activation functions and incorporates noise-tolerant techniques for handling different noises arising in TVQPPs. Besides, theoretical analyses show that the ZNN-based model globally converges to the time-varying optimization solution of TVQPPs in the presence of noises. In addition, an illustrative example is provided to substantiate the efficiency and robustness of the ZNN-based model for online solving TVQPPs with inherent tolerance to noises. Moreover, the ZNN-based model is applied to the economic model, which provides and investigates their computational efficiency and superiority. Finally, an application example to repetitive motion generation of four-wheel omnidirectional mobile robot is simulated to substantiate the feasibility and superiority of the developed NNSIZNN model for online solving TVQPPs with nonconvex constraints and measurement noise.