Nonconvex Noise-Tolerant Neural Model for Repetitive Motion of Omnidirectional Mobile Manipulators.

Dear Editor, Quadratic programming problems (QPs) receive a lot of attention in various fields of science computing and engineering applications, such as manipulator control [1]. Recursive neural network (RNN) is considered to be a powerful QPs solver due to its parallel processing capability and feasibility of hardware implementation [2]. In particular, a large number of RNN models, such as gradient neural network, are proposed as powerful alternatives for online solving QPs [3]. However, it is worth noting that most of the above neural networks are essentially designed for solving static QPs with time-invariant parameters. These neural algorithms cannot solve time-varying (TV) QPs because they cannot adapt to change in parameters, such as kinematic control of redundant arms [4]. Zeroing neural network (ZNN) is specially designed for real-time solution of time-varying problems. It uses the time derivative (TD) of time-varying parameters to solve the zero-finding problem [5]. The Taylor-type discrete-time ZNN (DTZNN) model is proposed in [6], which outperforms other models are inherently used to address the static QPs, such as Newton iterations. Although the DTZNN model makes full use of the TD information of the problem to be solved, it still does not explicitly consider the influence of noise. In the real-time solution of nonlinear system, there are system errors or external disturbances in hardware implementation, which can be regarded as noise [7]. Different RNN models are constructed by choosing different error functions (EFs) or utilizing different activation functions (AFs) in existing models, but the design process is roughly similar. However, the AF should be a monotone increasing odd function. Therefore, the ZNN-based model can be drawn by relaxing the convex constraint of the AF for TVQPs with equality and inequality constraints (EAICs) in the presence of noises.