Recurrent-Neural-Network-Based Polynomial Noise Resistance Model for Computing Dynamic Nonlinear Equations Applied to Robotics

The solution of dynamic nonlinear equations plays an important role in the control of complex systems. However, as a common physical phenomenon, noise seriously affects the effectiveness of online solutions in the form of external disturbance, inaccurate modeling, or estimation errors. In reality, most noises have different values at different moments and can be described by a sufficiently high-order nonlinear function. Such a function can theoretically be fitted or approximated by a sufficiently high-order polynomial. Nevertheless, existing models may lose their solving ability in the face of such high-order polynomial noise, which greatly limits their applications. To this end, a generalized RNN-based polynomial noise resistance (RB-PNR) model is proposed to learn the characteristic of noises with their order and coefficients unknown and then eliminate them accurately in solving dynamic nonlinear equations. Theoretical analysis and numerical simulation results demonstrate that the RB-PNR design model achieves zero residual error under polynomial noise disturbance with unknown order and coefficients. In addition, applications on different robots and the design of a 2-D digital filter are conducted to verify further the excellent robustness and physical realization of the designed RB-PNR model.