Rejecting Chaotic Disturbances Using a Super-Exponential-Zeroing Neurodynamic Approach for Synchronization of Chaotic Sensor Systems
Abstract
:1. Introduction
- By making progress along the direction of the CZN approach, the paper proposes an effective SEZN approach and its associated controller to promote the convergence properties, and accelerate the synchronization process of chaotic sensor systems.
- The controller designed by the proposed SEZN approach distinctively and inherently possesses the advantage of super-exponential convergence, which makes the synchronization process faster and more accurate. It is a breakthrough in the convergence research of the neurodynamic approach and real-time chaotic synchronization of sensor systems.
- Theoretical analyses on the stability and convergence advantages in terms of both faster convergence speed and lower error bound within the synchronization duration are shown in detail to guarantee the validity and advantage of the SEZN approach and its associated controller.
- Simulation studies including three synchronization examples, comparisons with other methods as well as extensive tests all verify the effectiveness as well as superiority of the SEZN approach and the related controller in practice.
2. Preliminaries and Neurodynamic Approaches
2.1. Synchronization of Chaotic Systems
2.2. Neurodynamic Approaches
3. Theoretical Analyses
4. Verifications, Comparisons and Tests
4.1. Synchronization Examples
4.1.1. Synchronization of Two Identical Lu Chaotic Systems
4.1.2. Synchronization of Two Identical Autonomous Chaotic Systems
4.1.3. Synchronization of Two Nonidentical Chaotic Systems
4.2. Comparisons with Other Approaches
4.3. Extensive Tests
5. Conclusions and Future Work
Author Contributions
Funding
Conflicts of Interest
References
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State of Chaotic Systems | |||||
---|---|---|---|---|---|
Element 1 of (24) and (25) | s | s | s | s | s |
Element 2 of (24) and (25) | s | s | s | s | s |
Element 3 of (24) and (25) | s | s | s | s | s |
State of Chaotic Systems | |||||
---|---|---|---|---|---|
Element 1 of (27) and (28) | s | s | s | s | s |
Element 2 of (27) and (28) | s | s | s | s | s |
Element 3 of (27) and (28) | s | s | s | s | s |
State of Chaotic Systems | |||||
---|---|---|---|---|---|
Element 1 of (24) and (28) | s | s | s | s | s |
Element 2 of (24) and (28) | s | s | s | s | s |
Element 3 of (24) and (28) | s | s | s | s | s |
State of Chaotic Systems | Number of Iterations | Estimation Time for Synchronization ◊ |
---|---|---|
Element 1 of (24) and (25) | 2377 | s |
Element 2 of (24) and (25) | 2378 | s |
Element 3 of (24) and (25) | 2377 | s |
Element 1 of (27) and (28) | 2191 | s |
Element 2 of (27) and (28) | 2191 | s |
Element 3 of (27) and (28) | 2190 | s |
Element 1 of (24) and (28) | 2377 | s |
Element 2 of (24) and (28) | 2377 | s |
Element 3 of (24) and (28) | 2377 | s |
Approach | Synchronization Speed | Convergence Property | Parameter Limitation |
---|---|---|---|
Proposed SEZN | Super-exponential | Global | No |
CZN | Exponential | Global | No |
[14] | Asymptotic | Global | Yes |
[53] | Exponential | Global | No |
[55] | Exponential | Global | No |
[56] | Exponential | Global | No |
[71] | Exponential | Global | No |
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Chen, D.; Li, S.; Wu, Q. Rejecting Chaotic Disturbances Using a Super-Exponential-Zeroing Neurodynamic Approach for Synchronization of Chaotic Sensor Systems. Sensors 2019, 19, 74. https://doi.org/10.3390/s19010074
Chen D, Li S, Wu Q. Rejecting Chaotic Disturbances Using a Super-Exponential-Zeroing Neurodynamic Approach for Synchronization of Chaotic Sensor Systems. Sensors. 2019; 19(1):74. https://doi.org/10.3390/s19010074
Chicago/Turabian StyleChen, Dechao, Shuai Li, and Qing Wu. 2019. "Rejecting Chaotic Disturbances Using a Super-Exponential-Zeroing Neurodynamic Approach for Synchronization of Chaotic Sensor Systems" Sensors 19, no. 1: 74. https://doi.org/10.3390/s19010074
APA StyleChen, D., Li, S., & Wu, Q. (2019). Rejecting Chaotic Disturbances Using a Super-Exponential-Zeroing Neurodynamic Approach for Synchronization of Chaotic Sensor Systems. Sensors, 19(1), 74. https://doi.org/10.3390/s19010074