The weights and structure determination (WASD) neuronet (or neural network) is a single-hidden-layer feedforward neuronet that exhibits an excellent approximation ability, despite its simple structure. Thanks to its strong generalization, fast speed, and ease of implementation, the WASD neuronet has been the subject of many modifications, including metaheuristics, and applications in a wide range of scientific fields. As it has garnered significant attention in the last decade, the aim of this study is to provide an extensive overview of the WASD framework. Furthermore, the WASD has been effectively used in numerous real-time learning tasks like regression, multiclass classification, and binary classification due to its exceptional performance. In addition, we present WASD’s applications in social science, business, engineering, economics, and medicine. We aim to report these developments and provide some avenues for further research.

Solving Lur'e equations plays a critical role in addressing linear-quadratic optimal control (LQOC) problems, especially in cases where the control cost matrices are singular. This paper introduces, for the first time, two novel zeroing neural network (ZNN) models—ZNNLE and ZNNLE-LQOC—specifically designed to solve the Lur'e equation system and the LQOC problem, respectively. The proposed models extend the applicability of the ZNN methodology to these challenging scenarios by offering robust and efficient solutions to time-varying matrix equations. Theoretical analyses confirm the validity of both models, while numerical simulations and practical applications demonstrate their effectiveness. Moreover, a comparative study with an enhanced alternating-direction implicit (ADI) method highlights the superior performance of the ZNNLE-LQOC model in solving LQOC problems.

Neurodynamics is recognized as a powerful tool for addressing various problems in engineering, control, and intelligent systems. Over the past decade, neurodynamics-based methods and models have been rapidly developed, particularly in emerging areas such as neural computation and multi-agent systems. In this paper, we provide a brief survey of neurodynamics applied to computation and multi-agent systems. Specifically, we highlight key models and approaches related to time-varying computation, as well as cooperative and competitive behaviors in multi-agent systems. Furthermore, we discuss current challenges, potential opportunities, and promising future directions in this evolving field.

Given the critical role of zeroing neural networks (ZNN) in various fields and the practical demand for models in effectively resisting real-time noise, this study introduces a novel anti-noise integral zeroing neural network (AN-IZNN) model alongside its enhanced counterpart (EAN-IZNN), for the applications of matrix problem solving. Theoretical analysis demonstrates their ability to achieve convergence even under different noise conditions. Both theoretical analyses and simulation validations highlight the superior performance of the proposed models over existing neural network models. Notably, the root mean square error of the proposed AN-IZNN and EAN-IZNN models is reduced by 92.6249% and 91.4178%, respectively, compared to scenarios without the proposed method, demonstrating the effectiveness of the solution.