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This work investigates the problem of future linear equation system under various noises. Firstly, a continuous advanced zeroing neurodynamic (CAZN) model under noise is developed to solve continuous linear equation system. Subsequently, by combining a general explicit linear left–right four-step (ELLRFS) formula with the CAZN model, a general ELLRFS discrete advanced zeroing neurodynamic (ELLRFS-DAZN) algorithm under noise is proposed to solve the future linear equation system. Theoretical analyses and results manifest the convergence performance of the general ELLRFS-DAZN algorithm under various noises. Moreover, numerical experimental results, including those based on a UR5 manipulator, validate the effectiveness and robustness of the general ELLRFS-DAZN algorithm under various noises. Numerical experimental results based on mobile acoustic source localization further substantiate the superiority of the general ELLRFS-DAZN algorithm under constant noise. Finally, physical experimental results based on a Kinova JACO2 manipulator substantiate the practicability of the general ELLRFS-DAZN algorithm under bounded random noise. [ABSTRACT FROM AUTHOR]

In this paper, discrete-time nonlinear optimization (DTNO) for tracking control of robot manipulators is investigated. By utilizing zeroing neural dynamics (ZND) method, a continuous-time ZND (CTZND) model is first proposed for solving the corresponding continuous-time nonlinear optimization (CTNO) problem. Afterwards, three different explicit linear multi-step methods (i.e., explicit linear 3-step, 2-step, and 1-step methods) are respectively presented and investigated. To solve such a DTNO problem, the explicit linear 3-step method is adopted to combine with the CTZND model, and hence a 3-step discrete-time ZND (DTZND) model is proposed. For comparison purposes, 2-step and 1-step DTZND models are also developed. Besides, theoretical analyses indicate the validity and superiority of the proposed 3-step DTZND model. Finally, the numerical experimental results based on a 2-joint robot manipulator and a PUMA560 robot manipulator further verify that the proposed 3-step DTZND model is much superior to the other two DTZND models. [ABSTRACT FROM AUTHOR]

This study investigated the problem of QR decomposition for time-varying matrices. We transform the original QR decomposition problem into an equation system using its constraints. Then, we propose a continuous-time QR decomposition (CTQRD) model by applying zeroing neural network method, equivalent transformations, Kronecker product, and vectorization techniques. Subsequently, a high-precision ten-instant Zhang et al. discretization (ZeaD) formula is proposed. A ten-instant discrete-time QR decomposition model is also proposed by using the ten-instant ZeaD formula to discretize the CTQRD model. Moreover, three discrete-time QR decomposition models are proposed by applying three other ZeaD formulas, and three examples of QR decomposition are presented. The experimental results confirm the effectiveness and correctness of the proposed models for the QR decomposition of time-varying matrices. [ABSTRACT FROM AUTHOR]

Future minimization, or say, discrete-time time-varying minimization, can be successfully solved by discrete-time Zhang neuronet (DTZN) models. A DTZN model is obtained through the discretization of a continuous-time Zhang neuronet (CTZN) model. However, most of the existing numerical differentiation formulas cannot be applied to discretizing a CTZN model for obtaining an effective DTZN model. Zhang et al discretization (ZeaD) formulas are the ones that can successfully address the problem about discretization. Recently, the four-point general ZeaD formula has been proposed (Hu et al., 2018), which can be applied to obtaining the four-point general DTZN model for future minimization. This paper focuses on researching the step-width-related stability of the four-point general DTZN model for future minimization. The step-width is a crucial parameter in the DTZN model. If the step-width is out of its corresponding interval, DTZN model does not converge in terms of residual error and fails in solving future minimization problem. By using Jury stability criterion, the analytic solution of step-width interval is proposed corresponding to the four-point general DTZN model. In addition, the optimal value of step-width is investigated, and the analytic solution of the optimal value is proposed as well. When step-width is equal to the optimal value, DTZN model has the fastest convergence rate to steady state with respect to residual error, and is farthest from instable state, thus having the best stability. The theoretical analyses are consistent with previous special-case investigations, and their correctness is confirmed by numerical experiments and results (i.e., numerics). [ABSTRACT FROM AUTHOR]