Delay-Dependent Exponential Optimal Synchronization for Nonidentical Chaotic Systems via Neural-Network-Based Approach
A novel approach is presented to realize the optimal exponential synchronization of nonidentical multiple time-delay chaotic (MTDC) systems via fuzzy control scheme. A neural-network (NN) model is first constructed for the MTDC system. Then, a linear differential inclusion (LDI) state-space represe...
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/294892 |
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| author | Feng-Hsiag Hsiao |
| author_facet | Feng-Hsiag Hsiao |
| author_sort | Feng-Hsiag Hsiao |
| collection | DOAJ |
| description | A novel approach is presented to realize the optimal exponential synchronization of nonidentical multiple time-delay chaotic (MTDC) systems via fuzzy control scheme. A neural-network (NN) model is first constructed for 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, a delay-dependent exponential stability criterion of the error system derived in terms of Lyapunov's direct method is proposed to guarantee 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). According to 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 at the same time. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach. |
| format | Article |
| id | doaj-art-b0bf25ef27b3417bb1b855398bcae889 |
| 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-b0bf25ef27b3417bb1b855398bcae8892025-08-20T03:39:15ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/294892294892Delay-Dependent Exponential Optimal Synchronization for Nonidentical Chaotic Systems via Neural-Network-Based ApproachFeng-Hsiag Hsiao0Department of Electrical Engineering, National University of Tainan, 33, Section 2, Shu Lin Street, Tainan 700, TaiwanA novel approach is presented to realize the optimal exponential synchronization of nonidentical multiple time-delay chaotic (MTDC) systems via fuzzy control scheme. A neural-network (NN) model is first constructed for 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, a delay-dependent exponential stability criterion of the error system derived in terms of Lyapunov's direct method is proposed to guarantee 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). According to 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 at the same time. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach.http://dx.doi.org/10.1155/2013/294892 |
| spellingShingle | Feng-Hsiag Hsiao Delay-Dependent Exponential Optimal Synchronization for Nonidentical Chaotic Systems via Neural-Network-Based Approach Abstract and Applied Analysis |
| title | Delay-Dependent Exponential Optimal Synchronization for Nonidentical Chaotic Systems via Neural-Network-Based Approach |
| title_full | Delay-Dependent Exponential Optimal Synchronization for Nonidentical Chaotic Systems via Neural-Network-Based Approach |
| title_fullStr | Delay-Dependent Exponential Optimal Synchronization for Nonidentical Chaotic Systems via Neural-Network-Based Approach |
| title_full_unstemmed | Delay-Dependent Exponential Optimal Synchronization for Nonidentical Chaotic Systems via Neural-Network-Based Approach |
| title_short | Delay-Dependent Exponential Optimal Synchronization for Nonidentical Chaotic Systems via Neural-Network-Based Approach |
| title_sort | delay dependent exponential optimal synchronization for nonidentical chaotic systems via neural network based approach |
| url | http://dx.doi.org/10.1155/2013/294892 |
| work_keys_str_mv | AT fenghsiaghsiao delaydependentexponentialoptimalsynchronizationfornonidenticalchaoticsystemsvianeuralnetworkbasedapproach |