Discrete time-variant equation systems represent a typical and complex problem across various disciplines. With the increasing complexity of systems in various fields, traditional methods have been unable to effectively deal with the current discrete time-variant equation systems, especially in the dynamic engineering problem. Generally speaking, traditional methods are typically limited to considering discrete time-variant equation systems in ideal state, and there is a lack of deep research about more intricate disturbance states. This paper introduces a new recurrent neural network (RNN) algorithm, termed the discrete-time double-integration-enhanced RNN (DT-DIE-RNN) algorithm, for handling discrete time-variant equation systems (including discrete time-variant linear and nonlinear equation system) under discrete square-time-variant disturbance. Firstly, the continuous-time double-integration-enhanced RNN (CT-DIE-RNN) algorithm is presented for solving discrete time-variant linear and nonlinear equation systems by using double-integral-type error function. Secondly, the corresponding discrete-time RNN algorithm is presented, and the convergence and precision of such an algorithm are theoretically analyzed. Finally, the effectiveness and superiority of the proposed DT-DIE-RNN algorithm for solving discrete time-variant linear and nonlinear equation systems are supported by comparative numerical experiments, and these theoretical results are further verified by robot manipulator applications. Note to Practitioners—Generally speaking, previous algorithms are unable to guarantee the operation of robot manipulator stably with discrete square-time-variant disturbance. In this study, we design a new RNN algorithm which possesses stronger anti-disturbance capability for solving discrete time-variant equation systems, and such the algorithm is applied to the tracking control of robot manipulator. In the discrete-time environment, in order to solve the discrete time-variant problem smoothly and stably, it is necessary to ensure that the error in each time period is within an acceptable range. The basic guidelines of this paper are as follows. First of all, a double-integration RNN algorithm is constructed, i.e., discrete-time double-integration-enhanced RNN (DT-DIE-RNN) algorithm. Then the effectiveness and superiority of the DT-DIE-RNN algorithm are verified by numerical experiment and engineering simulation, respectively. In summary, the proposed RNN algorithm can be seen as a new breakthrough in the research field of discrete-time RNN algorithm.

Our goal is to investigate and exploit an analogy between the scaled hyperpower family (SHPI family) of iterative methods for computing the matrix inverse and the discretization of Zhang Neural Network (ZNN) models. A class of ZNN models corresponding to the family of hyperpower iterative methods for computing generalized inverses is defined on the basis of the discovered analogy. The Simulink implementation in Matlab of the introduced ZNN models is described in the case of scaled hyperpower methods of the order 2 and 3. Convergence properties of the proposed ZNN models are investigated as well as their numerical behavior.

A new recurrent neural network is presented for solving linear algebraic systems with finite‐time convergence. The proposed model includes an exponential term in the Zhang neural network dynamical system, which leads to a faster convergence of the error‐monitoring function in comparison to previous methods. Theoretical analysis, as well as simulation results, validate the efficacy of the proposed model.