Nonsingular Terminal Sliding Mode Control Based on Adaptive Barrier Function for <i>n</i><sup>th</sup>-Order Perturbed Nonlinear Systems
In this study, an adaptive nonsingular finite time control technique based on a barrier function terminal sliding mode controller is proposed for the robust stability of <i>n</i><sup>th</sup>-order nonlinear dynamic systems with external disturbances. The barrier function ada...
| Main Authors: | , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-12-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/1/43 |
| _version_ | 1797498333120430080 |
|---|---|
| author | Khalid A. Alattas Javad Mostafaee Abdullah K. Alanazi Saleh Mobayen Mai The Vu Anton Zhilenkov Hala M. Abo-Dief |
| author_facet | Khalid A. Alattas Javad Mostafaee Abdullah K. Alanazi Saleh Mobayen Mai The Vu Anton Zhilenkov Hala M. Abo-Dief |
| author_sort | Khalid A. Alattas |
| collection | DOAJ |
| description | In this study, an adaptive nonsingular finite time control technique based on a barrier function terminal sliding mode controller is proposed for the robust stability of <i>n</i><sup>th</sup>-order nonlinear dynamic systems with external disturbances. The barrier function adaptive terminal sliding mode control makes the convergence of tracking errors to a region near zero in the finite time. Moreover, the suggested method does not need the information of upper bounds of perturbations which are commonly applied to the sliding mode control procedure. The Lyapunov stability analysis proves that the errors converge to the determined region. Last of all, simulations and experimental results on a complex new chaotic system with a high Kaplan–Yorke dimension are provided to confirm the efficacy of the planned method. The results demonstrate that the suggested controller has a stronger tracking than the adaptive controller and the results are satisfactory with the application of the controller based on chaotic synchronization on the chaotic system. |
| first_indexed | 2024-03-10T03:32:57Z |
| format | Article |
| id | doaj.art-8aff85ac3a13494ba312e356eae8163b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:32:57Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8aff85ac3a13494ba312e356eae8163b2023-11-23T11:53:14ZengMDPI AGMathematics2227-73902021-12-011014310.3390/math10010043Nonsingular Terminal Sliding Mode Control Based on Adaptive Barrier Function for <i>n</i><sup>th</sup>-Order Perturbed Nonlinear SystemsKhalid A. Alattas0Javad Mostafaee1Abdullah K. Alanazi2Saleh Mobayen3Mai The Vu4Anton Zhilenkov5Hala M. Abo-Dief6Department of Computer Science and Artificial Intelligence, College of Computer Science and Engineering, University of Jeddah, Jeddah 23890, Saudi ArabiaFuture Technology Research Center, National Yunlin University of Science and Technology, Douliou, Yunlin 64002, TaiwanDepartment of Chemistry, Faculty of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaFuture Technology Research Center, National Yunlin University of Science and Technology, Douliou, Yunlin 64002, TaiwanSchool of Intelligent Mechatronics Engineering, Sejong University, Seoul 05006, KoreaDepartment of Cyber-Physical Systems, St. Petersburg State Marine Technical University, 190121 Saint-Petersburg, RussiaDepartment of Chemistry, Faculty of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaIn this study, an adaptive nonsingular finite time control technique based on a barrier function terminal sliding mode controller is proposed for the robust stability of <i>n</i><sup>th</sup>-order nonlinear dynamic systems with external disturbances. The barrier function adaptive terminal sliding mode control makes the convergence of tracking errors to a region near zero in the finite time. Moreover, the suggested method does not need the information of upper bounds of perturbations which are commonly applied to the sliding mode control procedure. The Lyapunov stability analysis proves that the errors converge to the determined region. Last of all, simulations and experimental results on a complex new chaotic system with a high Kaplan–Yorke dimension are provided to confirm the efficacy of the planned method. The results demonstrate that the suggested controller has a stronger tracking than the adaptive controller and the results are satisfactory with the application of the controller based on chaotic synchronization on the chaotic system.https://www.mdpi.com/2227-7390/10/1/43nonlinear systemsliding mode controladaptive functionchaotic systemfinite time synchronization |
| spellingShingle | Khalid A. Alattas Javad Mostafaee Abdullah K. Alanazi Saleh Mobayen Mai The Vu Anton Zhilenkov Hala M. Abo-Dief Nonsingular Terminal Sliding Mode Control Based on Adaptive Barrier Function for <i>n</i><sup>th</sup>-Order Perturbed Nonlinear Systems Mathematics nonlinear system sliding mode control adaptive function chaotic system finite time synchronization |
| title | Nonsingular Terminal Sliding Mode Control Based on Adaptive Barrier Function for <i>n</i><sup>th</sup>-Order Perturbed Nonlinear Systems |
| title_full | Nonsingular Terminal Sliding Mode Control Based on Adaptive Barrier Function for <i>n</i><sup>th</sup>-Order Perturbed Nonlinear Systems |
| title_fullStr | Nonsingular Terminal Sliding Mode Control Based on Adaptive Barrier Function for <i>n</i><sup>th</sup>-Order Perturbed Nonlinear Systems |
| title_full_unstemmed | Nonsingular Terminal Sliding Mode Control Based on Adaptive Barrier Function for <i>n</i><sup>th</sup>-Order Perturbed Nonlinear Systems |
| title_short | Nonsingular Terminal Sliding Mode Control Based on Adaptive Barrier Function for <i>n</i><sup>th</sup>-Order Perturbed Nonlinear Systems |
| title_sort | nonsingular terminal sliding mode control based on adaptive barrier function for i n i sup th sup order perturbed nonlinear systems |
| topic | nonlinear system sliding mode control adaptive function chaotic system finite time synchronization |
| url | https://www.mdpi.com/2227-7390/10/1/43 |
| work_keys_str_mv | AT khalidaalattas nonsingularterminalslidingmodecontrolbasedonadaptivebarrierfunctionforinisupthsuporderperturbednonlinearsystems AT javadmostafaee nonsingularterminalslidingmodecontrolbasedonadaptivebarrierfunctionforinisupthsuporderperturbednonlinearsystems AT abdullahkalanazi nonsingularterminalslidingmodecontrolbasedonadaptivebarrierfunctionforinisupthsuporderperturbednonlinearsystems AT salehmobayen nonsingularterminalslidingmodecontrolbasedonadaptivebarrierfunctionforinisupthsuporderperturbednonlinearsystems AT maithevu nonsingularterminalslidingmodecontrolbasedonadaptivebarrierfunctionforinisupthsuporderperturbednonlinearsystems AT antonzhilenkov nonsingularterminalslidingmodecontrolbasedonadaptivebarrierfunctionforinisupthsuporderperturbednonlinearsystems AT halamabodief nonsingularterminalslidingmodecontrolbasedonadaptivebarrierfunctionforinisupthsuporderperturbednonlinearsystems |