Design, verification and robotic application of a novel recurrent neural network for computing dynamic Sylvester equation

To solve dynamic Sylvester equation in the presence of additive noises, a novel recurrent neural network (NRNN) with finite-time convergence and excellent robustness is proposed and analyzed in this paper. As compared with the design process of Zhang neural network (ZNN), the proposed NRNN is based on an ingenious integral design formula activated by nonlinear functions, which are able to expedite the convergence speed and suppress unknown additive noises during the solving process of dynamic Sylvester equation. In addition, the global stability, finite-time convergence and denoising property of the NRNN model are theoretically proved. The upper bound of the finite convergence time for the NRNN model is also estimated in theory. Simulative results further verify the efficiency of the NRNN model, as well as its superior robust and finite-time performance to the conventional ZNN model for dynamic Sylvester equation in front of additive noises. At last, the proposed design method for establishing the NRNN model is successfully applied to kinematical control of robotic manipulator in front of additive noises.