Optimal Exponential Synchronization of Chaotic Systems with Multiple Time Delays via Fuzzy Control
This study presents an effective approach to realize the optimal exponential synchronization of multiple time-delay chaotic (MTDC) systems. First, a neural network (NN) model is employed to approximate the MTDC system. Then, a linear differential inclusion (LDI) state-space representation is establ...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/742821 |
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| _version_ | 1832563832313085952 |
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| author | Feng-Hsiag Hsiao |
| author_facet | Feng-Hsiag Hsiao |
| author_sort | Feng-Hsiag Hsiao |
| collection | DOAJ |
| description | This study presents an effective approach to realize the optimal exponential synchronization of multiple time-delay chaotic (MTDC) systems. First, a neural network (NN) model is employed to approximate the MTDC system. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on this LDI state-space representation, this study proposes a delay-dependent exponential stability criterion of the error system derived in terms of Lyapunov’s direct method to ensure that the trajectories of the slave system can approach those of the master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). Based on the LMI, a fuzzy controller is synthesized not only to realize the exponential synchronization but also to achieve the optimal performance by minimizing the disturbance attenuation level. Finally, a numerical example with simulations is provided to illustrate the concepts discussed throughout this work. |
| format | Article |
| id | doaj-art-2683b7a253d5452ea664eda6e7dbc50b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2683b7a253d5452ea664eda6e7dbc50b2025-02-03T01:12:26ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/742821742821Optimal Exponential Synchronization of Chaotic Systems with Multiple Time Delays via Fuzzy ControlFeng-Hsiag Hsiao0Department of Electrical Engineering, National University of Tainan, No. 33, Section 2, Shu Lin Street, Tainan 700, TaiwanThis study presents an effective approach to realize the optimal exponential synchronization of multiple time-delay chaotic (MTDC) systems. First, a neural network (NN) model is employed to approximate the MTDC system. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on this LDI state-space representation, this study proposes a delay-dependent exponential stability criterion of the error system derived in terms of Lyapunov’s direct method to ensure that the trajectories of the slave system can approach those of the master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). Based on the LMI, a fuzzy controller is synthesized not only to realize the exponential synchronization but also to achieve the optimal performance by minimizing the disturbance attenuation level. Finally, a numerical example with simulations is provided to illustrate the concepts discussed throughout this work.http://dx.doi.org/10.1155/2013/742821 |
| spellingShingle | Feng-Hsiag Hsiao Optimal Exponential Synchronization of Chaotic Systems with Multiple Time Delays via Fuzzy Control Abstract and Applied Analysis |
| title | Optimal Exponential Synchronization of Chaotic Systems with Multiple Time Delays via Fuzzy Control |
| title_full | Optimal Exponential Synchronization of Chaotic Systems with Multiple Time Delays via Fuzzy Control |
| title_fullStr | Optimal Exponential Synchronization of Chaotic Systems with Multiple Time Delays via Fuzzy Control |
| title_full_unstemmed | Optimal Exponential Synchronization of Chaotic Systems with Multiple Time Delays via Fuzzy Control |
| title_short | Optimal Exponential Synchronization of Chaotic Systems with Multiple Time Delays via Fuzzy Control |
| title_sort | optimal exponential synchronization of chaotic systems with multiple time delays via fuzzy control |
| url | http://dx.doi.org/10.1155/2013/742821 |
| work_keys_str_mv | AT fenghsiaghsiao optimalexponentialsynchronizationofchaoticsystemswithmultipletimedelaysviafuzzycontrol |