Low-Complexity ZNN Model Handling Time-Varying Generalized Matrix Inversion Problems with Multilayered Sensor-Related Disturbances Applied to Robot Manipulator

Sensor-related disturbances and measurement uncertainties often degrade the performance of dynamic neural network methods in solving time-varying problems, especially the time-varying generalized matrix inversion (TVGMI) problem, which serves as the computational foundation for real-time control and signal reconstruction tasks. Traditional zeroing neural network (ZNN) models for handling TVGMI problems usually require matrix inversion or vectorization operations, leading to high computational complexity and poor robustness under sensor disturbance or time-varying perturbations. To overcome these challenges, this article proposes a novel low-complexity ZNN (LCZNN) model that achieves efficient and unified computation of time-varying matrix inversion and pseudoinverse without involving inverse matrix computation. To further enhance robustness, the LCZNN model is extended to handle multilayered sensor-related disturbances, giving rise to three variants: the state-disturbed LCZNN (SDLCZNN), the velocity-disturbed LCZNN (VDLCZNN), and the hybrid-disturbed LCZNN (HDLCZNN) models. Each variant introduces structured compensation dynamics that enable accurate convergence under different disturbance scenarios. Rigorous theoretical analyses establish their convergence and stability properties. Comprehensive numerical experiments on representative TVGMI problems validate the low computational burden, fast convergence, and superior multilayered disturbance tolerance of the proposed LCZNN framework. Moreover, discrete algorithms derived via Euler discretization are applied to the real-time path-tracking inverse-kinematics control of robotic manipulators. Simulation and physical experimental results confirm that the proposed LCZNN-based algorithms achieve high tracking precision, strong robustness, and computational efficiency, making them well-suited for real-time robotic and control applications.