Event-Triggered Discrete-Time ZNN Algorithm for Distributed Optimization with Time-Varying Objective Functions
Abstract
:1. Introduction
- An innovative ET-CTZNN model is introduced to tackle the CTDTVO problem. The ET-CTZNN model operates within a semi-centralized framework, solving the CTDTVO problem in continuous time.
- The ET-CTZNN model is discretized using the Euler formula to develop the fully distributed ET-DTZNN algorithm. The ET-DTZNN algorithm enables agents to compute optimal solutions based on local time-varying objective functions and exchange state information with neighbors only when specific event-triggered conditions are met, significantly reducing communication consumption.
- Comprehensive theoretical analyses are conducted, establishing the convergence of both the ET-CTZNN model and the ET-DTZNN algorithm, ensuring their effectiveness in solving the DTVO problem.
2. Preliminaries and Problem Formulation for DTDTVO
2.1. Preliminaries
2.2. Problem Formulation for DTDTVO
3. Event-Triggered Continuous-Time ZNN Model
3.1. Continuous-Time ZNN Model
3.2. Event-Triggered Continuous-Time ZNN Model
4. Event-Triggered Discrete-Time ZNN Algorithm
4.1. Semi-Centralized ET-DTZNN Model
4.2. Fully Distributed ET-DTZNN Algorithm
5. Theoretical Analyses
5.1. Convergence Theorem for ET-CTZNN Model
5.2. Robustness and Zeno Behavior Analysis for ET-CTZNN Model
5.2.1. Analysis on Robustness for ET-CTZNN Model
- Case 1: If , then we obtain , which implies that tends to decrease and converges towards . That is, .
- Case 2: If , then we obtain . (i) When , we determine that is a decreasing function, which implies that is less than , and the situation turns into Case 3. (ii) When , it indicates that remains on the surface of a sphere with a radius of . That is, .
- Case 3: If , then we have . (i) When , we determine that is a decreasing function, which indicates that . (ii) When , it indicates that remains on the surface of a sphere with a radius of less than . That is, . (iii) When , we determine that is an increasing function, which indicates that the residual error tends to converge towards as time increases. That is, .
5.2.2. Analysis on Zeno Behavior for ET-CTZNN Model
5.3. Convergence Theorems of ET-DTZNN Algorithm
6. Numerical Experiments
6.1. Example 1: DTDTVO Problem Solved by ET-DTZNN Algorithm
6.2. Example 2: Comparative Experiments
6.3. Example 3: DTDTVO Problem Solved by ET-DTZNN Algorithm in Large MASs
6.3.1. ET-DTZNN in Large MAS Under Static Topology
6.3.2. ET-DTZNN in Large MAS Under Dynamic Topology
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
DTVO | Distributed Time-Varying Optimization |
MASs | Multi-Agent Systems |
ZNN | Zeroing Neural Network |
CTDTVO | Continuous-Time Distributed Time-Varying Optimization |
DTDTVO | Discrete-Time Distributed Time-Varying Optimization |
CTZNN | Continuous-Time Zeroing Neural Network |
DTZNN | Discrete-Time Zeroing Neural Network |
ET-CTZNN | Event-Triggered Continuous-Time Zeroing Neural Network |
ET-DTZNN | Event-Triggered Discrete-Time Zeroing Neural Network |
MSSRE | Maximum Steady-State Residual Error |
MSSD | Maximum Steady-State Deviation |
GNN | Gradient Neural Network |
PSGNN | Periodic Sampling Gradient Neural Network |
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Expression | |
---|---|
MSSRE | |
---|---|
0.001 s | |
0.0005 s | |
0.0001 s |
Agent | Number of Trigger Events with | Number of Trigger Events with | Number of Trigger Events with | Number of Trigger Events with |
---|---|---|---|---|
Agent 1 | 1915 | 1840 | 1404 | 1289 |
Agent 2 | 5141 | 1614 | 1512 | 1444 |
Agent 3 | 4867 | 1598 | 1439 | 1304 |
Agent 4 | 6459 | 2417 | 2156 | 1968 |
Agent 5 | 6161 | 2312 | 2345 | 2132 |
MSSRE of PSGNN | MSSRE of ET-DTZNN | |
---|---|---|
0.001 s | ||
0.0005 s | ||
0.0001 s |
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He, L.; Cheng, H.; Zhang, Y. Event-Triggered Discrete-Time ZNN Algorithm for Distributed Optimization with Time-Varying Objective Functions. Electronics 2025, 14, 1359. https://doi.org/10.3390/electronics14071359
He L, Cheng H, Zhang Y. Event-Triggered Discrete-Time ZNN Algorithm for Distributed Optimization with Time-Varying Objective Functions. Electronics. 2025; 14(7):1359. https://doi.org/10.3390/electronics14071359
Chicago/Turabian StyleHe, Liu, Hui Cheng, and Yunong Zhang. 2025. "Event-Triggered Discrete-Time ZNN Algorithm for Distributed Optimization with Time-Varying Objective Functions" Electronics 14, no. 7: 1359. https://doi.org/10.3390/electronics14071359
APA StyleHe, L., Cheng, H., & Zhang, Y. (2025). Event-Triggered Discrete-Time ZNN Algorithm for Distributed Optimization with Time-Varying Objective Functions. Electronics, 14(7), 1359. https://doi.org/10.3390/electronics14071359