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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]

Future quadratic programming (FQP) is an interesting and challenging topic due to its unknown future information and time-dependent feature. In this paper, a continuous-time zeroing neurodynamics (CTZN) model for quadratic programming is first obtained via zeroing neurodynamics (ZN) method. Then, a general four-step Zhang et al. discretization formula is presented and adopted to discretize the above CTZN model, and thus the general four-step discrete-time ZN (DTZN) algorithm for the FQP is developed. For comparison, a three-step DTZN algorithm and a one-step DTZN algorithm for the FQP are also presented. It is worth noting that there is an important parameter termed stepsize in the DTZN algorithms, which is closely related to their stability. If the value of stepsize is outside its effective interval, the DTZN algorithms are impossible to achieve convergence in terms of residual errors, which leads to failure of the FQP problem solving. By utilizing bilinear transformation and Routh stability criterion, the effective stepsize interval of the general four-step DTZN algorithm is confirmed via theoretical proof. Besides, numerical results substantiate the effectiveness and superiority of the general four-step DTZN algorithm as well as the accuracy of the effective stepsize interval. Finally, the general four-step DTZN algorithm is applied to fulfill the path-tracking control of different robot manipulators, with the effectiveness and superiority further validated. [ABSTRACT FROM AUTHOR]

In this paper, a new five-step discrete-time zeroing dynamics (DTZD) algorithm, discretized from a continuous-time zeroing dynamics (CTZD) model, is proposed and investigated for online future nonlinear minimization (OFNM), i.e., online discrete-time dynamic nonlinear minimization. For approximating more accurately the first-order derivative and discretizing more effectively the CTZD model, a six-node g-cube discretization (6Ng CD) formula with higher precision is presented to obtain the new five-step DTZD algorithm. Besides, the corresponding theoretical result shows that the proposed five-step DTZD algorithm is with a quartic steady-state error pattern, i.e., O(g4) pattern, with g denoting the sampling gap. Moreover, a general DTZD algorithm is constructed by applying the general linear multistep method, and a specific DTZD algorithm based on the 4th-order Adams-Bashforth method (termed DTZD-AB algorithm for short) is further developed for OFNM. Several numerical experiments are conducted to substantiate the efficacy, accuracy, and superiority of the proposed five-step DTZD algorithm (as well as the DTZD-AB algorithm) for solving the OFNM problem, as compared with the one-step and three-step DTZD algorithms developed and investigated in previous works. [ABSTRACT FROM AUTHOR]