A neural network algorithm for superstructure quadrilateral dynamic resistor networks on hammock surfaces with application to artificial intelligence

Abstract

This study proposes a fast zeroing neural network algorithm to solve time-varying Laplacian linear systems arising from the modeling of superstructure quadrilateral dynamic resistor networks on hammock surfaces. By incorporating the intrinsic structure of the underlying special-form matrices into the core neurodynamic design, the proposed algorithm enables efficient real-time computation of electric potentials under dynamic conditions. The Lyapunov-based analysis proves global exponential convergence. Numerical simulations on resistor networks of various scales demonstrate high computational efficiency and verify convergence to solutions from arbitrary initial conditions. Furthermore, by integrating the proposed algorithm as a potential field solver with a directional potential field path planning algorithm and exploiting the natural descent property of resistor network node potentials, we propose a fast path planning algorithm for robotic navigation on hammock surfaces. Compared with conventional path planning approaches, the proposed algorithm achieves higher computational efficiency in the aforementioned hammock surface path planning task, and this advantage becomes increasingly pronounced as the scale increases. The proposed algorithm is also applied to dynamic path planning tasks, further validating its potential in robotics and control applications. Finally, we present two conjectures.

Keywords

Zeroing neural network / Resistor network / Laplacian system / Equivalent resistance / Potential / Path planning

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