Discrete-time Zeroing Neural Network with Quintic Error Mode for Time-Dependent Nonlinear Equation and Its Application to Robot Arms

Time-dependent nonlinear equation (TDNE) arises in numerous engineering applications. Recently, zeroing neural network (ZNN) has been proven to be an effective alternative for solving the TDNE. In this paper, we present a new solution to the TDNE by using the discrete-time ZNN (DTZNN). Specifically, a special difference formula is first constructed via Taylor series expansion. Then, by utilizing such a formula to discretize the existing continuous-time ZNN model, the new DTZNN model is proposed to determine the TDNE solution. Theoretical analysis and numerical results further indicate the validity and superiority of the proposed DTZNN model in comparison with the previous models. Finally, the DTZNN practicality is presented by the simulation and experiment on the DOBOT arm using the proposed model.