A Fuzzy-Power Direct-Discretization RNN Algorithm for Solving Discrete Multilayer Dynamic Systems With Robotic Applications

This work proposes a new recurrent neural network (RNN) algorithm for solving discrete multilayer dynamic systems (DMDSs). First, by utilizing the direct-discretization technique, a direct-discretization RNN (DDRNN) algorithm for solving the DMDSs is introduced. On this basis, a fuzzy-power direct-discretization RNN (FDDRNN) algorithm is proposed, which integrates a fuzzy control system (FCS) within the DDRNN framework. This integration dynamically modulates the time step τ by exerting a fuzzy-power factor r, which is determined based on the logarithm of the residual, as τ<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup>. Finally, comparative evaluations among the gradient-based RNN (GBRNN), the DDRNN, and the FDDRNN algorithms are conducted through numerical experiments and robotic application experiments involving both planar and spatial robots. The results indicate that the proposed FDDRNN algorithm outperforms the GBRNN and DDRNN algorithms in terms of accuracy, convergence speed, and stability.