A Modified Structured Spectral HS Method for Nonlinear Least Squares Problems and Applications in Robot Arm Control
This paper proposes a modification to the Hestenes-Stiefel (HS) method by devising a spectral parameter using a modified secant relation to solve nonlinear least-squares problems. Notably, in the implementation, the proposed method differs from existing approaches, in that it does not require a safe...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-07-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/14/3215 |
| _version_ | 1797588426188390400 |
|---|---|
| author | Rabiu Bashir Yunus Nooraini Zainuddin Hanita Daud Ramani Kannan Samsul Ariffin Abdul Karim Mahmoud Muhammad Yahaya |
| author_facet | Rabiu Bashir Yunus Nooraini Zainuddin Hanita Daud Ramani Kannan Samsul Ariffin Abdul Karim Mahmoud Muhammad Yahaya |
| author_sort | Rabiu Bashir Yunus |
| collection | DOAJ |
| description | This paper proposes a modification to the Hestenes-Stiefel (HS) method by devising a spectral parameter using a modified secant relation to solve nonlinear least-squares problems. Notably, in the implementation, the proposed method differs from existing approaches, in that it does not require a safeguarding strategy and its Hessian matrix is positive and definite throughout the iteration process. Numerical experiments are conducted on a range of test problems, with 120 instances to demonstrate the efficacy of the proposed algorithm by comparing it with existing techniques in the literature. However, the results obtained validate the effectiveness of the proposed method in terms of the standard metrics of comparison. Additionally, the proposed approach is applied to address motion-control problems in a robotic model, resulting in favorable outcomes in terms of the robot’s motion characteristics. |
| first_indexed | 2024-03-11T00:51:50Z |
| format | Article |
| id | doaj.art-778246bc62c74e2b86cdc23a04da299d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T00:51:50Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-778246bc62c74e2b86cdc23a04da299d2023-11-18T20:22:18ZengMDPI AGMathematics2227-73902023-07-011114321510.3390/math11143215A Modified Structured Spectral HS Method for Nonlinear Least Squares Problems and Applications in Robot Arm ControlRabiu Bashir Yunus0Nooraini Zainuddin1Hanita Daud2Ramani Kannan3Samsul Ariffin Abdul Karim4Mahmoud Muhammad Yahaya5Department of Fundamental and Applied Sciences, Faculty of Science and Information Technology, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, Perak Darul Ridzuan, MalaysiaDepartment of Fundamental and Applied Sciences, Faculty of Science and Information Technology, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, Perak Darul Ridzuan, MalaysiaDepartment of Fundamental and Applied Sciences, Faculty of Science and Information Technology, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, Perak Darul Ridzuan, MalaysiaDepartment of Electrical and Electronics Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, Perak Darul Ridzuan, MalaysiaSoftware Engineering Programme, Faculty of Computing and Informatics, Universiti Malaysia Sabah, Jalan UMS, Kota Kinabalu 88400, Sabah, MalaysiaDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, ThailandThis paper proposes a modification to the Hestenes-Stiefel (HS) method by devising a spectral parameter using a modified secant relation to solve nonlinear least-squares problems. Notably, in the implementation, the proposed method differs from existing approaches, in that it does not require a safeguarding strategy and its Hessian matrix is positive and definite throughout the iteration process. Numerical experiments are conducted on a range of test problems, with 120 instances to demonstrate the efficacy of the proposed algorithm by comparing it with existing techniques in the literature. However, the results obtained validate the effectiveness of the proposed method in terms of the standard metrics of comparison. Additionally, the proposed approach is applied to address motion-control problems in a robotic model, resulting in favorable outcomes in terms of the robot’s motion characteristics.https://www.mdpi.com/2227-7390/11/14/3215conjugate gradientiterative algorithmnonlinear least-squaressecant equationrobotic modelquasi-Newton |
| spellingShingle | Rabiu Bashir Yunus Nooraini Zainuddin Hanita Daud Ramani Kannan Samsul Ariffin Abdul Karim Mahmoud Muhammad Yahaya A Modified Structured Spectral HS Method for Nonlinear Least Squares Problems and Applications in Robot Arm Control Mathematics conjugate gradient iterative algorithm nonlinear least-squares secant equation robotic model quasi-Newton |
| title | A Modified Structured Spectral HS Method for Nonlinear Least Squares Problems and Applications in Robot Arm Control |
| title_full | A Modified Structured Spectral HS Method for Nonlinear Least Squares Problems and Applications in Robot Arm Control |
| title_fullStr | A Modified Structured Spectral HS Method for Nonlinear Least Squares Problems and Applications in Robot Arm Control |
| title_full_unstemmed | A Modified Structured Spectral HS Method for Nonlinear Least Squares Problems and Applications in Robot Arm Control |
| title_short | A Modified Structured Spectral HS Method for Nonlinear Least Squares Problems and Applications in Robot Arm Control |
| title_sort | modified structured spectral hs method for nonlinear least squares problems and applications in robot arm control |
| topic | conjugate gradient iterative algorithm nonlinear least-squares secant equation robotic model quasi-Newton |
| url | https://www.mdpi.com/2227-7390/11/14/3215 |
| work_keys_str_mv | AT rabiubashiryunus amodifiedstructuredspectralhsmethodfornonlinearleastsquaresproblemsandapplicationsinrobotarmcontrol AT noorainizainuddin amodifiedstructuredspectralhsmethodfornonlinearleastsquaresproblemsandapplicationsinrobotarmcontrol AT hanitadaud amodifiedstructuredspectralhsmethodfornonlinearleastsquaresproblemsandapplicationsinrobotarmcontrol AT ramanikannan amodifiedstructuredspectralhsmethodfornonlinearleastsquaresproblemsandapplicationsinrobotarmcontrol AT samsulariffinabdulkarim amodifiedstructuredspectralhsmethodfornonlinearleastsquaresproblemsandapplicationsinrobotarmcontrol AT mahmoudmuhammadyahaya amodifiedstructuredspectralhsmethodfornonlinearleastsquaresproblemsandapplicationsinrobotarmcontrol AT rabiubashiryunus modifiedstructuredspectralhsmethodfornonlinearleastsquaresproblemsandapplicationsinrobotarmcontrol AT noorainizainuddin modifiedstructuredspectralhsmethodfornonlinearleastsquaresproblemsandapplicationsinrobotarmcontrol AT hanitadaud modifiedstructuredspectralhsmethodfornonlinearleastsquaresproblemsandapplicationsinrobotarmcontrol AT ramanikannan modifiedstructuredspectralhsmethodfornonlinearleastsquaresproblemsandapplicationsinrobotarmcontrol AT samsulariffinabdulkarim modifiedstructuredspectralhsmethodfornonlinearleastsquaresproblemsandapplicationsinrobotarmcontrol AT mahmoudmuhammadyahaya modifiedstructuredspectralhsmethodfornonlinearleastsquaresproblemsandapplicationsinrobotarmcontrol |