1. From Gauss–Newton method solving nonlinear least squares problem of static overdetermined system to multi-instant neurodynamic algorithms handling future time-variant situation.
- Author
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Wu, Dongqing and Zhang, Yunong
- Abstract
Gauss–Newton method is mainly designed and exploited to solve the nonlinear least squares problems of static overdetermined systems with order-2 precision. When the system comes to the future time-variant situation, the disadvantages of the Gauss–Newton method in effectiveness and precision need to be overcome. On the basis of Zhang neurodynamics, the first Zhang neurodynamics model and the second Zhang neurodynamics model are constructed and discussed to obtain the nonlinear least squares solution of the time-variant overdetermined system in the future time-variant situation. Then, we propose a novel eleven-instant Zhang time discretization formula whose convergenceness and truncation errors of order-6 are proved through rigorous mathematical derivation. The proposed eleven-instant Zhang time discretization formula is thus utilized to discretize the constructed first Zhang neurodynamics model and second Zhang neurodynamics model, respectively. Consequently, a novel discrete-time eleven-instant first Zhang neurodynamics-based algorithm and a novel discrete-time eleven-instant second Zhang neurodynamics-based algorithm are proposed and generalized to obtain the predictive nonlinear least squares solution of the time-variant overdetermined system in the future time-variant situation. Furthermore, the precisions of the proposed discrete-time eleven-instant first Zhang neurodynamics-based and second Zhang neurodynamics-based algorithms are proved to be of order-6 through mathematical derivation. Moreover, this work reveals the facts that the Gauss–Newton method is actually the simplified version of the discrete-time two-instant first Zhang neurodynamics-based algorithm and the discrete-time two-instant second Zhang neurodynamics-based algorithm, respectively. Finally, five challenging numerical experiments, including the problem-solving of the critical force of a crane in a complicated environment, are carried out. The experimental results further substantiate the applicability and superiority of the proposed discrete-time eleven-instant first Zhang neurodynamics-based and second Zhang neurodynamics-based algorithms in the future time-variant situation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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