A review of Zeroing neural network: Theory, algorithm and application

As a powerful method for solving complex computational equations, neural networks have attracted widespread attention due to their unique advantages. However, due to the existence of time-varying problems in practical applications, traditional Gradient neural network (GNN) models may not be able to satisfy the requirements for accurately solving such problems, leading to the emergence of a dynamic system solution method - Zeroing neural network (ZNN), a dynamic system solver designed specifically for solving various time-varying mathematical problems and real-time control applications. ZNN eliminates errors through the use of dynamic differential equations, fundamentally overcoming the limitations of GNN in effectively converging for time-varying problems. Additionally, considering different application demands in practical scenarios and interference from noise in realistic environments, various robust ZNN models with different convergence properties have emerged. This paper will summarize the development of ZNN models in recent years from theoretical foundation, algorithm improvement and practical application aspects, and finally prospect the future research directions of ZNN models to provide researchers with a systematic reference.