Consensus Control of Leader–Follower Multi-Agent Systems with Unknown Parameters and Its Circuit Implementation
Abstract
:1. Introduction
- (1)
- The dynamic characteristics of the financial system are analyzed, and the results show that the system behavior can be effectively controlled through the parameters of the financial system.
- (2)
- According to Lyapunov stability theorem, linear state feedback controllers are designed to synchronize financial systems. Meanwhile, adaptive control laws are derived for synchronization of master–slave systems with unknown parameters, and numerical simulations are given to verify the theoretical results.
- (3)
- The consensus theorem of leader–follower multi-agent systems is proved based on complex financial systems. The circuit implementation of master–slave systems consensus is provided through variable synchronization and parameter identification.
2. Dynamic Analysis of the Financial System
2.1. Equilibrium Point of Financial System (1)
2.2. Bifurcation Analysis of Financial System (1)
Algorithm 1: Algorithm of Bifurcation with Respect to Parameter c |
|
3. Consensus Control of Master–Slave Systems
3.1. Consensus Control of Master–Slave Financial Systems
3.2. Consensus of Master–Slave Systems with Unknown Parameters
4. Consensus of Leader–Follower Multi-Agent Systems with Unknown Parameters
4.1. Consensus of Leader–Follower Multi-Agent Systems
4.2. Numerical Simulations
4.3. Discussions of the Consensus for Multi-Agent Systems
- (1)
- The controller with only a linear term and a gain coefficient is simple and easy to implement;
- (2)
- The number of controllers is fewer, and only the first and second equations of slave financial system are added controllers;
- (3)
- The control cost is relatively low, and the linear feedback controller is easy to implement in hardware, such as the circuit implementation of master–slave synchronization.
5. Circuit Implementation
5.1. Circuit Implementation of the Financial System
5.2. Circuit Implementation of Master–Slave Systems
5.3. Circuit Implementation of Master–Slave Systems with Unknown Parameters
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Agent | Initial Errors ,, in Equation (20) | Control Time t When , | Control Costs of , and Total Cost |
---|---|---|---|
1 | 0.1, 0.1, 0.2 | 14.19, 12.00 | {812.92, 311.68}, 1124.60 |
2 | 0.0, 0.9, 1.2 | 12.29, 8.49 | {1640.54, 1600.14}, 3240.68 |
3 | 1.1, 0.6, 1.2 | 21.98, 18.21 | {1814.09, 1145.51}, 2959.60 |
4 | 0.5, 0.4, 1.1 | 22.01, 20.24 | {1806.64, 1418.36}, 3225.00 |
Agent | Initial Errors , , in Equation (21) | Control Time t When , | The Costs of , and Total Cost |
---|---|---|---|
1 | 0.1, 0.1, 0.3 | 10.79, 12.02, 11.57 | {116.36,173.33,429.40}, 719.09 |
2 | 0.2, 0.3, 0.4 | 5.55, 8.43, 10.94 | {215.86,990.61,922.13}, 2128.60 |
3 | 0.19, 0.25, 0.36 | 17.88, 12.72, 15.14 | {348.54,796.55,790.29}, 1935.38 |
4 | 0.22, 0.4, 0.4 | 17.90, 12.76, 15.40 | {348.38,1042.67,1013.86}, 2404.91 |
Agent | Initial Errors in Equation (20) of , | Control Time t When , | Control Costs of , and Total Cost |
---|---|---|---|
3 | 1.1, 0.6, 1.2 | 21.98, 17.00 | {2228.17, 848.90}, 3077.07 |
5 | 0.4, 0.2, 0.2 | 14.24, 7.74 | {4149.07, 2747.63}, 6896.70 |
Agent | Initial Errors , , in Equation (21) | Control Time t When | The Costs of , and Total Cost |
---|---|---|---|
3 | 0.19, 0.25, 0.36 | 14.15, 8.11, 15.29 | {198.92,704.98,466.67}, 1370.57 |
5 | 0.32, 0.3, 0.3 | 14.50, 16.54, 15.39 | {355.26,673.66,967.35}, 1996.27 |
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Ye, Y.; He, J. Consensus Control of Leader–Follower Multi-Agent Systems with Unknown Parameters and Its Circuit Implementation. Appl. Sci. 2024, 14, 8894. https://doi.org/10.3390/app14198894
Ye Y, He J. Consensus Control of Leader–Follower Multi-Agent Systems with Unknown Parameters and Its Circuit Implementation. Applied Sciences. 2024; 14(19):8894. https://doi.org/10.3390/app14198894
Chicago/Turabian StyleYe, Yinfang, and Jianbin He. 2024. "Consensus Control of Leader–Follower Multi-Agent Systems with Unknown Parameters and Its Circuit Implementation" Applied Sciences 14, no. 19: 8894. https://doi.org/10.3390/app14198894