New Noise-Tolerant ZNN Models With Predefined-Time Convergence for Time-Variant Sylvester Equation Solving

Sylvester equation is often applied to various fields, such as mathematics and control systems due to its importance. Zeroing neural network (ZNN), as a systematic design method for time-variant problems, has been proved to be effective on solving Sylvester equation in the ideal conditions. In this paper, in order to realize the predefined-time convergence of the ZNN model and modify its robustness, two new noise-tolerant ZNNs (NNTZNNs) are established by devising two novelly constructed nonlinear activation functions (AFs) to find the accurate solution of the time-variant Sylvester equation in the presence of various noises. Unlike the original ZNN models activated by known AFs, the proposed two NNTZNN models are activated by two novel AFs, therefore, possessing the excellent predefined-time convergence and strong robustness even in the presence of various noises. Besides, the detailed theoretical analyses of the predefined-time convergence and robustness ability for the NNTZNN models are given by considering different kinds of noises. Simulation comparative results further verify the excellent performance of the proposed NNTZNN models, when applied to online solution of the time-variant Sylvester equation

Proposing, developing and verification of a novel discrete-time zeroing neural network for solving future augmented Sylvester matrix equation

In this paper, a novel discrete-time advance zeroing neural network (DT-AZNN) model is proposed, developed and investigated for solving future augmented Sylvester matrix equation (F-ASME). First of all, based on the advance zeroing neural network (AZNN) design formula, a novel continuous-time advance zeroing neural network (CT-AZNN) model is shown for solving continuous-time augmented Sylvester matrix equation (CT-ASME). Secondly, a recently published discretization formula is further investigated with the optimal sampling gap of the discretization formula proposed. Then, for solving F-ASME, a novel DT-AZNN model is proposed based on the discretization formula. Theoretical analyses on the convergence property and the perturbation suppression performance of the DT-AZNN model are provided. Moreover, comparative numerical experimental results are conducted to prove the effectiveness and robustness of the proposed DT-AZNN model for solving F-ASME

Design and Comprehensive Analysis of a Noise-Tolerant ZNN Model With Limited-Time Convergence for Time-Dependent Nonlinear Minimization

Zeroing neural network (ZNN) is a powerful tool to address the mathematical and optimization problems broadly arisen in the science and engineering areas. The convergence and robustness are always co-pursued in ZNN. However, there exists no related work on the ZNN for time-dependent nonlinear minimization that achieves simultaneously limited-time convergence and inherently noise suppression. In this article, for the purpose of satisfying such two requirements, a limited-time robust neural network (LTRNN) is devised and presented to solve time-dependent nonlinear minimization under various external disturbances. Different from the previous ZNN model for this problem either with limited-time convergence or with noise suppression, the proposed LTRNN model simultaneously possesses such two characteristics. Besides, rigorous theoretical analyses are given to prove the superior performance of the LTRNN model when adopted to solve time-dependent nonlinear minimization under external disturbances. Comparative results also substantiate the effectiveness and advantages of LTRNN via solving a time-dependent nonlinear minimization problem