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In this paper, firstly, a high accuracy one-step-ahead numerical differentiation formula with O(τ 4) pattern is proposed for discretization. Meanwhile, a high precision first-order derivative formula of the backward difference rule with O(τ 4) pattern error is given to approximate the derivative information. Then, two high accuracy discrete-time zeroing-type models (HADTZTM) with O(τ 4) pattern, i.e., HADTZTM with derivative information known (HADTZTM-K) and HADTZTM with derivative information unknown (HADTZTM-U), are developed, analyzed and investigated for online solving the dynamic system of linear equations (DSLEs). In addition, the 0-stability, consistency, and convergence of the HADTZTM-K and HADTZTM-U are verified for DSLEs. From a theoretical/numerical viewpoint, the classical models are revisited and analyzed for online solving DSLEs. Ultimately, simulation experiment including an application to the path-tracking of the four-link planar manipulator is conducted to demonstrate the efficiency and superiority of the HADTZTM-K and HADTZTM-U, where the HADTZTM-U overcomes the difficulty of derivative information unknown in practical applications. INDEX TERMS Dynamic system of linear equations (DSLEs), discrete-time zeroing neural network (DTZNN), backward difference formula, theoretical results, steady-state residual error.

In this paper, the adaptive fuzzy neural network (AFNN) based on the surface electromyography (sEMG) for estimating the elbow joint angle is established and investigated from the perspective of rapidity and accuracy. In addition, back propagation neural network (BPNN) and artificial neural network of radial basis function (RBFNN), as the classical method for data forecasting, have been applied to estimate the elbow joint angle for comparing with AFNN. Ultimately, the experimental simulation and result analysis demonstrate that the rapidity and accuracy of AFNN is superior to BPNN and RBFNN.

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