Structured zeroing neural network solution for the mathematical model of a fan dynamic resistor network and its applications

Resistor networks are key tools in interdisciplinary research, however, dynamic resistor networks have not been thoroughly studied. In this study, we introduce a structured zeroing neural network model to tackle the mathematical model of fan dynamic resistor networks, thus filling the research gap in the field of dynamic resistor networks. This study integrates the inherent structural characteristics of special matrices with the core layer in the design of dynamic system algorithms, and accordingly devises a class of fast algorithms for this neural network model. Under identical experimental settings, the computational efficiency of the proposed model is 300–500 times higher than that of conventional methods, and its convergence speed is also improved. The neural network model is further employed to compute the equivalent resistance between any two points in fan resistor networks. Furthermore, this study incorporates the physical property of the natural descent of electric potential into robot path planning, and proposes a robot path planning method tailored to fan-shaped curved surface environments. Compared with traditional path-planning approaches, the proposed method attains higher computational efficiency in such scenarios, as the network scale grows, the advantages of our path planning algorithms become increasingly prominent, highlighting the method’s excellent scalability. Finally, we propose two conjectures.