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Modified Newton integration algorithm with noise suppression for online dynamic nonlinear optimization

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Abstract

The solution of nonlinear optimization is usually encountered in many fields of scientific researches and engineering applications, which spawns a large number of corresponding algorithms to cope with it. Besides, with developments of modern cybernetics technology, it imperatively requires some advanced numerical algorithms to solve online dynamic nonlinear optimization (ODNO). Nevertheless, the major existing algorithms are limited to the static nonlinear optimization models, few works considering the dynamic ones, let alone tolerating noise. For the abovementioned reasons, this paper proposes a modified Newton integration (MNI) algorithm for ODNO with strong robustness and high-accuracy computing solution, which can effectively suppress the influence caused by noise components. In addition, the correlative theoretical analyses and mathematical proofs on convergence and robustness of the MNI algorithm are carried out, which indicates that computing solutions of the proposed MNI algorithm can globally converge to relative small value in the presence of various noise or zero noise conditions. Finally, to illustrate the advantages and feasibilities of the proposed MNI algorithm for ODNO problems, four numerical simulation examples and an application to robot manipulator motion generation are performed.

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Funding

This work is supported by the Fund of Southern Marine Science and Engineering Guangdong Laboratory of Zhanjiang, China under Grant ZJW-2019-08, by the Key Projects of the Guangdong Education Department under Grant 2019KZDXM019, in part by the High-Level Marine Discipline Team Project of Guangdong Ocean University under Grant 002026002009, by the Guangdong Graduate Academic Forum Project under Grant 230420003, by the “First Class” Discipline Construction Platform Project in 2019 of Guangdong Ocean University under Grant 231419026, by the Innovation and Strength Project in Guangdong Province, China (Natural Science) under Grant 230419065, by the Key Lab of Digital Signal and Image Processing of Guangdong Province, China under Grant 2019GDDSIPL-01, by the Industry-University-Research Cooperation Education Project of Ministry of Education under Grant 201801328005, by the Guangdong Graduate Education Innovation Project, Graduate Summer School under Grant 2020SQXX19, by the Guangdong Graduate Education Innovation Project, Graduate Academic Forum under Grant 2020XSLT27, by the Doctoral Initiating Project of Guangdong Ocean University under Grant E13428, and also by the Special Project in Key Fields of Universities in Department of Education of Guangdong Province, China under Grant 2019033.

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Authors and Affiliations

  1. School of Electronics and Information Engineering, Guangdong Ocean University (GDOU), Zhanjiang, 524025, China

    Haoen Huang, Dongyang Fu & Huan Wang

  2. Department of Computer and Information Science, Faculty of Science and Technology, University of Macau, Macau, 999078, China

    Guancheng Wang

  3. School of Electronics and Information Engineering, Guangdong Ocean University, Zhanjiang, 524088, China

    Long Jin

  4. Shenzhen Institute of Guangdong Ocean University, Guangdong Ocean University, Shenzhen, 518108, China

    Long Jin

  5. School of Information Science and Engineering, Lanzhou University, Lanzhou, 730000, China

    Long Jin

  6. School of Cybersecurity, Sichuan University, Chengdu, 610065, China

    Shan Liao

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  1. Haoen Huang
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Correspondence to Dongyang Fu.

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Huang, H., Fu, D., Wang, G. et al. Modified Newton integration algorithm with noise suppression for online dynamic nonlinear optimization. Numer Algor 87, 575–599 (2021). https://doi.org/10.1007/s11075-020-00979-6

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