Integration-Enhanced Zhang Neural Network for Real-Time-Varying Matrix Inversion in the Presence of Various Kinds of Noises

Matrix inversion often arises in the fields of science and engineering. Many models for matrix inversion usually assume that the solving process is free of noises or that the denoising has been conducted before the computation. However, time is precious for the real-time-varying matrix inversion in practice, and any preprocessing for noise reduction may consume extra time, possibly violating the requirement of real-time computation. Therefore, a new model for time-varying matrix inversion that is able to handle simultaneously the noises is urgently needed. In this paper, an integration-enhanced Zhang neural network (IEZNN) model is first proposed and investigated for real-time-varying matrix inversion. Then, the conventional ZNN model and the gradient neural network model are presented and employed for comparison. In addition, theoretical analyses show that the proposed IEZNN model has the global exponential convergence property. Moreover, in the presence of various kinds of noises, the proposed IEZNN model is proven to have an improved performance. That is, the proposed IEZNN model converges to the theoretical solution of the time-varying matrix inversion problem no matter how large the matrix-form constant noise is, and the residual errors of the proposed IEZNN model can be arbitrarily small for time-varying noises and random noises. Finally, three illustrative simulation examples, including an application to the inverse kinematic motion planning of a robot manipulator, are provided and analyzed to substantiate the efficacy and superiority of the proposed IEZNN model for real-time-varying matrix inversion.