Regional PID Control of Switched Positive Systems With Multiple Equilibrium Points
This paper investigates the regional control problem of switched positive systems with multiple equilibrium points. A proportional-integral-derivative controller is designed by combining the output, the error between the state and the equilibrium point, and the difference of output. A cone is introd...
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| Format: | Article |
| Language: | English |
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IEEE
2024-01-01
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| Series: | IEEE Open Journal of Control Systems |
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| Online Access: | https://ieeexplore.ieee.org/document/10504945/ |
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| author | Pei Zhang Junfeng Zhang Xuan Jia |
| author_facet | Pei Zhang Junfeng Zhang Xuan Jia |
| author_sort | Pei Zhang |
| collection | DOAJ |
| description | This paper investigates the regional control problem of switched positive systems with multiple equilibrium points. A proportional-integral-derivative controller is designed by combining the output, the error between the state and the equilibrium point, and the difference of output. A cone is introduced to design the final stable region. Two classes of copositive Lyapunov functions are constructed to achieve the stability and regional stability of subsystems and the whole systems, respectively. Then, a novel class of observers with multiple equilibrium points is proposed using a matrix decomposition approach. The observer-based proportional-integral-derivative control problem is thus solved and all states are driven to the designed cone region under the designed controller. All conditions are formulated in the form of linear programming. The novelties of this paper lie in that: (i) A proportional-integral-derivative control framework is introduced for the considered systems, (ii) Luenberger observer is developed for the observer with multiple equilibrium points, and (iii) Copositive Lyapunov functions and linear programming are employed for the analysis and design of controller and observer. Finally, the effectiveness of the proposed design is verified via two examples. |
| format | Article |
| id | doaj-art-c80bbedee867433dbd011c0daad8e43d |
| institution | Kabale University |
| issn | 2694-085X |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Journal of Control Systems |
| spelling | doaj-art-c80bbedee867433dbd011c0daad8e43d2025-01-09T00:03:01ZengIEEEIEEE Open Journal of Control Systems2694-085X2024-01-01319020110.1109/OJCSYS.2024.339100110504945Regional PID Control of Switched Positive Systems With Multiple Equilibrium PointsPei Zhang0https://orcid.org/0009-0003-8627-5864Junfeng Zhang1https://orcid.org/0000-0003-1335-6682Xuan Jia2https://orcid.org/0000-0002-1705-4801School of Information and Communication Engineering, Hainan University, Haikou, ChinaSchool of Information and Communication Engineering, Hainan University, Haikou, ChinaSchool of Information and Communication Engineering, Hainan University, Haikou, ChinaThis paper investigates the regional control problem of switched positive systems with multiple equilibrium points. A proportional-integral-derivative controller is designed by combining the output, the error between the state and the equilibrium point, and the difference of output. A cone is introduced to design the final stable region. Two classes of copositive Lyapunov functions are constructed to achieve the stability and regional stability of subsystems and the whole systems, respectively. Then, a novel class of observers with multiple equilibrium points is proposed using a matrix decomposition approach. The observer-based proportional-integral-derivative control problem is thus solved and all states are driven to the designed cone region under the designed controller. All conditions are formulated in the form of linear programming. The novelties of this paper lie in that: (i) A proportional-integral-derivative control framework is introduced for the considered systems, (ii) Luenberger observer is developed for the observer with multiple equilibrium points, and (iii) Copositive Lyapunov functions and linear programming are employed for the analysis and design of controller and observer. Finally, the effectiveness of the proposed design is verified via two examples.https://ieeexplore.ieee.org/document/10504945/Switched positive systemsmultiple equilibrium pointsproportional-integral-derivative controllinear programming |
| spellingShingle | Pei Zhang Junfeng Zhang Xuan Jia Regional PID Control of Switched Positive Systems With Multiple Equilibrium Points IEEE Open Journal of Control Systems Switched positive systems multiple equilibrium points proportional-integral-derivative control linear programming |
| title | Regional PID Control of Switched Positive Systems With Multiple Equilibrium Points |
| title_full | Regional PID Control of Switched Positive Systems With Multiple Equilibrium Points |
| title_fullStr | Regional PID Control of Switched Positive Systems With Multiple Equilibrium Points |
| title_full_unstemmed | Regional PID Control of Switched Positive Systems With Multiple Equilibrium Points |
| title_short | Regional PID Control of Switched Positive Systems With Multiple Equilibrium Points |
| title_sort | regional pid control of switched positive systems with multiple equilibrium points |
| topic | Switched positive systems multiple equilibrium points proportional-integral-derivative control linear programming |
| url | https://ieeexplore.ieee.org/document/10504945/ |
| work_keys_str_mv | AT peizhang regionalpidcontrolofswitchedpositivesystemswithmultipleequilibriumpoints AT junfengzhang regionalpidcontrolofswitchedpositivesystemswithmultipleequilibriumpoints AT xuanjia regionalpidcontrolofswitchedpositivesystemswithmultipleequilibriumpoints |