Observer-Based H∞ Fuzzy Synchronization and Output Tracking Control of Time-Varying Delayed Chaotic Systems
Tracking control for the output using an observer-based H∞ fuzzy synchronization of time-varying delayed discrete- and continuous-time chaotic systems is proposed in this paper. First, from a practical point of view, the chaotic systems here consider the influence of time-varying delays, disturbance...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5918268 |
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| author | Kuan-Yi Lin Tung-Sheng Chiang Chian-Song Chiu Wen-Fong Hu Peter Liu |
| author_facet | Kuan-Yi Lin Tung-Sheng Chiang Chian-Song Chiu Wen-Fong Hu Peter Liu |
| author_sort | Kuan-Yi Lin |
| collection | DOAJ |
| description | Tracking control for the output using an observer-based H∞ fuzzy synchronization of time-varying delayed discrete- and continuous-time chaotic systems is proposed in this paper. First, from a practical point of view, the chaotic systems here consider the influence of time-varying delays, disturbances, and immeasurable states. Then, to facilitate a uniform control design approach for both discrete- and continuous-time chaotic systems, the dynamic models along with time-varying delays and disturbances are reformulated using the T-S (Takagi–Sugeno) fuzzy representation. For control design considering immeasurable states, a fuzzy observer achieves master-slave synchronization. Third, combining both a fuzzy observer for state estimation and a controller (solved from generalized kinematic constraints) output tracking can be achieved. To make the design more practical, we also consider differences of antecedent variables between the plant, observer, and controller. Finally, using Lyapunov’s stability approach, the results are sufficient conditions represented as LMIs (linear matrix inequalities). The contributions of the method proposed are threefold: (i) systemic and unified problem formulation of master-slave synchronization and tracking control for both discrete and continuous chaotic systems; (ii) practical consideration of time-varying delay, immeasurable state, different antecedent variables (of plant, observer, and controller), and disturbance in the control problem; and (iii) sufficient conditions from Lyapunov’s stability analysis represented as LMIs which are numerically solvable observer and controller gains from LMIs. We carry out numerical simulations on a chaotic three-dimensional discrete-time system and continuous-time Chua’s circuit. Satisfactory numerical results further show the validity of the theoretical derivations. |
| format | Article |
| id | doaj-art-ab210689b9ef4720bb5b1265e4d19587 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ab210689b9ef4720bb5b1265e4d195872025-02-03T01:04:17ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/59182685918268Observer-Based H∞ Fuzzy Synchronization and Output Tracking Control of Time-Varying Delayed Chaotic SystemsKuan-Yi Lin0Tung-Sheng Chiang1Chian-Song Chiu2Wen-Fong Hu3Peter Liu4Department of Electrical and Computer Engineering, Tamkang University, New Taipei City, TaiwanDepartment of Electrical Engineering, Chien Hsin University of Science and Technology, Taoyuan, TaiwanDepartment of Electrical Engineering, Chung-Yuan Christian University, Taoyuan, TaiwanDepartment of Electrical Engineering, Chien Hsin University of Science and Technology, Taoyuan, TaiwanDepartment of Electrical and Computer Engineering, Tamkang University, New Taipei City, TaiwanTracking control for the output using an observer-based H∞ fuzzy synchronization of time-varying delayed discrete- and continuous-time chaotic systems is proposed in this paper. First, from a practical point of view, the chaotic systems here consider the influence of time-varying delays, disturbances, and immeasurable states. Then, to facilitate a uniform control design approach for both discrete- and continuous-time chaotic systems, the dynamic models along with time-varying delays and disturbances are reformulated using the T-S (Takagi–Sugeno) fuzzy representation. For control design considering immeasurable states, a fuzzy observer achieves master-slave synchronization. Third, combining both a fuzzy observer for state estimation and a controller (solved from generalized kinematic constraints) output tracking can be achieved. To make the design more practical, we also consider differences of antecedent variables between the plant, observer, and controller. Finally, using Lyapunov’s stability approach, the results are sufficient conditions represented as LMIs (linear matrix inequalities). The contributions of the method proposed are threefold: (i) systemic and unified problem formulation of master-slave synchronization and tracking control for both discrete and continuous chaotic systems; (ii) practical consideration of time-varying delay, immeasurable state, different antecedent variables (of plant, observer, and controller), and disturbance in the control problem; and (iii) sufficient conditions from Lyapunov’s stability analysis represented as LMIs which are numerically solvable observer and controller gains from LMIs. We carry out numerical simulations on a chaotic three-dimensional discrete-time system and continuous-time Chua’s circuit. Satisfactory numerical results further show the validity of the theoretical derivations.http://dx.doi.org/10.1155/2021/5918268 |
| spellingShingle | Kuan-Yi Lin Tung-Sheng Chiang Chian-Song Chiu Wen-Fong Hu Peter Liu Observer-Based H∞ Fuzzy Synchronization and Output Tracking Control of Time-Varying Delayed Chaotic Systems Journal of Mathematics |
| title | Observer-Based H∞ Fuzzy Synchronization and Output Tracking Control of Time-Varying Delayed Chaotic Systems |
| title_full | Observer-Based H∞ Fuzzy Synchronization and Output Tracking Control of Time-Varying Delayed Chaotic Systems |
| title_fullStr | Observer-Based H∞ Fuzzy Synchronization and Output Tracking Control of Time-Varying Delayed Chaotic Systems |
| title_full_unstemmed | Observer-Based H∞ Fuzzy Synchronization and Output Tracking Control of Time-Varying Delayed Chaotic Systems |
| title_short | Observer-Based H∞ Fuzzy Synchronization and Output Tracking Control of Time-Varying Delayed Chaotic Systems |
| title_sort | observer based h∞ fuzzy synchronization and output tracking control of time varying delayed chaotic systems |
| url | http://dx.doi.org/10.1155/2021/5918268 |
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