New noise-tolerant neural algorithms for future dynamic nonlinear optimization with estimation on hessian matrix inversion

Wei, Lin; Jin, Long; Yang, Chenguang; Chen, Ke; Li, Weibing

Abstract

Nonlinear optimization problems with dynamical parameters are widely arising in many practical scientific and engineering applications, and various computational models are presented for solving them under the hypothesis of short-time invariance. To eliminate the large lagging error in the solution of the inherently dynamic nonlinear optimization problem, the only way is to estimate the future unknown information by using the present and previous data during the solving process, which is termed the future dynamic nonlinear optimization (FDNO) problem. In this paper, to suppress noises and improve the accuracy in solving FDNO problems, a novel noise-tolerant neural (NTN) algorithm based on zeroing neural dynamics is proposed and investigated. In addition, for reducing algorithm complexity, the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is employed to eliminate the intensively computational burden for matrix inversion, termed NTN-BFGS algorithm. Moreover, theoretical analyses are conducted, which show that the proposed algorithms are able to globally converge to a tiny error bound with or without the pollution of noises. Finally, numerical experiments are conducted to validate the superiority of the proposed NTN and NTN-BFGS algorithms for the online solution of FDNO problems.

• Journal Article Type: Article
• Acceptance Date: May 4, 2019
• Online Publication Date: May 27, 2019
• Publication Date: Apr 1, 2021
• Deposit Date: May 29, 2019
• Publicly Available Date: May 28, 2020
• Journal: IEEE Transactions on Systems, Man, and Cybernetics: Systems
• Print ISSN: 2168-2216
• Publisher: Institute of Electrical and Electronics Engineers
• Peer Reviewed: Peer Reviewed
• Volume: 51
• Issue: 4
• Pages: 2611 - 2623
• DOI: https://doi.org/10.1109/TSMC.2019.2916892
• Public URL: https://uwe-repository.worktribe.com/output/846629
• Publisher URL: http://doi.org/10.1109/TSMC.2019.2916892
• Additional Information: Additional Information : (c) 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
• Contract Date: May 29, 2019