An Integration-Enhanced Noise-Resistant RNN Model with Superior Performance Illustrated via Time-Varying Sylvester Equation Solving

The Sylvester equation plays a fundamental role in the control system, e.g, which can be applied to inverse-kinematic motion control problem in robot manipulators through a certain conversion. Considering the incompatibility of most existing Sylvester equation solving schemes on noise and the inevitability of noise in real life, by defining a new matrix-valued error function, an integration-enhanced noise-resistant recurrent neural network (IENRRNN) is generalize to the time-varying Sylvester equation solving in this paper. The convergence of the IENRRNN model under both the model implementation error and differential error of coefficient matrices are investigated. What’s more, from both convergence speed and convergence quality, effects of three activation functions on the computational errors achieved by the IENRRNN are evaluated. The influences of different design parameters on them are also discussed. Finally, with MATLAB, the effectiveness of the IENRRNN model for online solving the considered equation and its superiority compared to the traditional zeroing neural network (ZNN) model are demonstrated by simulative results.