Multi-Sided Delayed Impulsive Feedback Method for Controlling Chaos and Reducing Loss Ratio in Switched Arrival System with Switching Time Greater than 0
The switched arrival system is a typical hybrid system that is commonly used to simulate industrial control systems. The corresponding mathematical model and switching time are described. In order to be closer to the actual industrial control systems, the switching time is changed from 0 to greater...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/2/198 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832588049184194560 |
|---|---|
| author | Ming Chen Xueshuai Zhu |
| author_facet | Ming Chen Xueshuai Zhu |
| author_sort | Ming Chen |
| collection | DOAJ |
| description | The switched arrival system is a typical hybrid system that is commonly used to simulate industrial control systems. The corresponding mathematical model and switching time are described. In order to be closer to the actual industrial control systems, the switching time is changed from 0 to greater than 0. In this case, the system not only generates chaos but also system losses. For this purpose, firstly, the causes of system losses are analyzed. Secondly, the Poincare section is selected to define the control target—periodic orbits. And then, the delayed impulsive feedback method is improved for the system at a switching time greater than 0, and extended to each boundary in order to enhance the control effect. This not only controls chaos in the system but also reduces the loss ratio and detects periodic orbits. Finally, numerical simulations of the system orbits and loss ratio with and without implementing control are compared. The possible intervals for the optimal control coefficient under the same initial conditions are detected. Period-1 orbits are detected at switching times greater than 0, and the stability of system operation is verified. |
| format | Article |
| id | doaj-art-36580f55001648f8b73c0f2b40670973 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-36580f55001648f8b73c0f2b406709732025-01-24T13:39:43ZengMDPI AGMathematics2227-73902025-01-0113219810.3390/math13020198Multi-Sided Delayed Impulsive Feedback Method for Controlling Chaos and Reducing Loss Ratio in Switched Arrival System with Switching Time Greater than 0Ming Chen0Xueshuai Zhu1School of General Education, Hubei College of Chinese Medicine, Jingzhou 434020, ChinaSchool of Chemical and Environmental Engineering, China University of Mining and Technology, Beijing 100083, ChinaThe switched arrival system is a typical hybrid system that is commonly used to simulate industrial control systems. The corresponding mathematical model and switching time are described. In order to be closer to the actual industrial control systems, the switching time is changed from 0 to greater than 0. In this case, the system not only generates chaos but also system losses. For this purpose, firstly, the causes of system losses are analyzed. Secondly, the Poincare section is selected to define the control target—periodic orbits. And then, the delayed impulsive feedback method is improved for the system at a switching time greater than 0, and extended to each boundary in order to enhance the control effect. This not only controls chaos in the system but also reduces the loss ratio and detects periodic orbits. Finally, numerical simulations of the system orbits and loss ratio with and without implementing control are compared. The possible intervals for the optimal control coefficient under the same initial conditions are detected. Period-1 orbits are detected at switching times greater than 0, and the stability of system operation is verified.https://www.mdpi.com/2227-7390/13/2/198switched arrival systemswitching timecontrolling chaosreducing loss ratiodetecting periodic orbitsystem stability |
| spellingShingle | Ming Chen Xueshuai Zhu Multi-Sided Delayed Impulsive Feedback Method for Controlling Chaos and Reducing Loss Ratio in Switched Arrival System with Switching Time Greater than 0 Mathematics switched arrival system switching time controlling chaos reducing loss ratio detecting periodic orbit system stability |
| title | Multi-Sided Delayed Impulsive Feedback Method for Controlling Chaos and Reducing Loss Ratio in Switched Arrival System with Switching Time Greater than 0 |
| title_full | Multi-Sided Delayed Impulsive Feedback Method for Controlling Chaos and Reducing Loss Ratio in Switched Arrival System with Switching Time Greater than 0 |
| title_fullStr | Multi-Sided Delayed Impulsive Feedback Method for Controlling Chaos and Reducing Loss Ratio in Switched Arrival System with Switching Time Greater than 0 |
| title_full_unstemmed | Multi-Sided Delayed Impulsive Feedback Method for Controlling Chaos and Reducing Loss Ratio in Switched Arrival System with Switching Time Greater than 0 |
| title_short | Multi-Sided Delayed Impulsive Feedback Method for Controlling Chaos and Reducing Loss Ratio in Switched Arrival System with Switching Time Greater than 0 |
| title_sort | multi sided delayed impulsive feedback method for controlling chaos and reducing loss ratio in switched arrival system with switching time greater than 0 |
| topic | switched arrival system switching time controlling chaos reducing loss ratio detecting periodic orbit system stability |
| url | https://www.mdpi.com/2227-7390/13/2/198 |
| work_keys_str_mv | AT mingchen multisideddelayedimpulsivefeedbackmethodforcontrollingchaosandreducinglossratioinswitchedarrivalsystemwithswitchingtimegreaterthan0 AT xueshuaizhu multisideddelayedimpulsivefeedbackmethodforcontrollingchaosandreducinglossratioinswitchedarrivalsystemwithswitchingtimegreaterthan0 |