Double Features Zeroing Neural Network Model for Solving the Pseudoninverse of a Complex-Valued Time-Varying Matrix

Abstract

The solution of a complex-valued matrix pseudoinverse is one of the key steps in various science and engineering fields. Owing to its important roles, researchers had put forward many related algorithms. With the development of research, a time-varying matrix pseudoinverse received more attention than a time-invarying one, as we know that a zeroing neural network (ZNN) is an efficient method to calculate a pseudoinverse of a complex-valued time-varying matrix. Due to the initial ZNN (IZNN) and its extensions lacking a mechanism to deal with both convergence and robustness, that is, most existing research on ZNN models only studied the convergence and robustness, respectively. In order to simultaneously improve the double features (i.e., convergence and robustness) of ZNN in solving a complex-valued time-varying pseudoinverse, this paper puts forward a double features ZNN (DFZNN) model by adopting a specially designed time-varying parameter and a novel nonlinear activation function. Moreover, two nonlinear activation types of complex number are investigated. The global convergence, predefined time convergence, and robustness are proven in theory, and the upper bound of the predefined convergence time is formulated exactly. The results of the numerical simulation verify the theoretical proof, in contrast to the existing complex-valued ZNN models, the DFZNN model has shorter predefined convergence time in a zero noise state, and enhances robustness in different noise states. Both the theoretical and the empirical results show that the DFZNN model has better ability in solving a time-varying complex-valued matrix pseudoinverse. Finally, the proposed DFZNN model is used to track the trajectory of a manipulator, which further verifies the reliability of the model.

Fixed-Time Convergent Gradient Neural Network for Solving Online Sylvester Equation

“…In addition to the characteristic of parallel processing, RNN models can be implemented expediently by circuit components in the wake of the rapid development of field-programmable gate array and integrated circuit technology [13][14][15]. As the result of these two outstanding features, a growing number of RNN models that aim at solving the Sylvester equation and related problems (e.g., matrix pseudoinverse) have been successively put forward and discussed in recent years [16][17][18][19][20][21][22][23][24][25]. ZNN (zeroing neural network) and GNN (gradient neural network) are two popular RNN categories that are extensively investigated in the literature.…”

“…Correspondingly, two predefined-time convergent ZNN models are successfully constructed for solving the time-variant Sylvester equation. Some ZNN models with varying design parameters are constructed and applied to the dynamic Sylvester equation and matrix pseudoinversion/inversion with real or complex coefficient matrices [19][20][21][22][23][24][25]. Additionally, discrete-time ZNN models based on continuous ZNN models are also developed for Sylvester equation solving [26][27][28][29].…”

A Dynamic-Varying Parameter Enhanced ZNN Model for Solving Time-Varying Complex-Valued Tensor Inversion With Its Application to Image Encryption

“…The TVCMI has also been studied by many researchers [10]- [14]. For instance, a complex-valued Zhang neural network (CVZNN) was presented for solving the TVCMI [10]; Xiao et al [12] proposed a robust CVZNN model for solving the TVCMI of Moore-Penrose, and the robust CVZNN was applied to control robot manipulator; and Xiao et al [13] proposed a complex-valued nonlinear recurrent neural network (CVNRNN) model, which showed better convergence than the ZNN model and the gradient-based neural network (GNN) model.…”