A Segmented Activation Function-Based Zeroing Neural Network Model for Dynamic Sylvester Equation Solving and Robotic Manipulator Control

Traditional methods for solving the dynamic Sylvester equations suffer from challenges such as unsatisfactory convergence and sensitivity to noise. To address these limitations, a segmented activation function-based Zeroing neural network (SAF-ZNN) model is proposed in this paper. The segmented activation function consists of the power function, hyperbolic tangent function, and exponential function, and the SAF-ZNN model can effectively deal with various system errors of various sizes and types. Specifically, the SAF-ZNN model with power function is used to handle large errors, the SAF-ZNN model with hyperbolic tangent function is used to handle medium errors, and the SAF-ZNN model with exponential function is used to handle small errors. The whole proposed SAF-ZNN model achieves rapid convergence and strong robustness adaptively during the dynamic Sylvester equation solving. Theoretical analysis proves that the proposed SAF-ZNN model possesses global stability, finite-time convergence, and noise tolerance. Furthermore, both the simulation experiments and their application in robotic manipulator control validate the superior performance of the proposed SAF-ZNN model.