Adaptive Consensus of the Stochastic Leader-Following Multi-Agent System with Time Delay
For the multi-agent system with time delay and noise, the adaptive consensus of tracking control problems is discussed by the Lyapunov function. The main purpose of this study is to design an adaptive control protocol for the system, such that even if there exists time delay among agents, the protoc...
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| Format: | Article |
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MDPI AG
2023-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/16/3517 |
| _version_ | 1797583985248829440 |
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| author | Shoubo Jin Guanghui Zhang |
| author_facet | Shoubo Jin Guanghui Zhang |
| author_sort | Shoubo Jin |
| collection | DOAJ |
| description | For the multi-agent system with time delay and noise, the adaptive consensus of tracking control problems is discussed by the Lyapunov function. The main purpose of this study is to design an adaptive control protocol for the system, such that even if there exists time delay among agents, the protocol can still ensure the consensus of the stochastic system. The main contribution is to revise the protocols that were previously only applicable to system without time delay. Because the system is inevitably disrupted by time delay and noise during the interactive process, achieving coordination and consensus is difficult. To enable the followers to track the leader, a novel adaptive law depending on the Riccati equation is firstly proposed, and the adaptive law is different from previous mandatory control law completely depending on a known function. The ability to be altered online based on the state of system is a major feature of the adaptive law. When there are interactive noise and time delay between the followers and leader of the system, a special Lyapunov function is constructed to prove the adaptive consensus. And the upper bound of time delay is obtained by using the Itô integral theory. Finally, if the time delay of the system approaches zero, it is shown that the adaptive law still ensures that each follower tracks the leader under simpler conditions. |
| first_indexed | 2024-03-10T23:45:57Z |
| format | Article |
| id | doaj.art-c655e50d97224dcda3d4a0c017345ef6 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T23:45:57Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c655e50d97224dcda3d4a0c017345ef62023-11-19T02:03:10ZengMDPI AGMathematics2227-73902023-08-011116351710.3390/math11163517Adaptive Consensus of the Stochastic Leader-Following Multi-Agent System with Time DelayShoubo Jin0Guanghui Zhang1School of Mathematics and Statistics, Suzhou University, Suzhou 234000, ChinaSchool of Mathematics and Statistics, Suzhou University, Suzhou 234000, ChinaFor the multi-agent system with time delay and noise, the adaptive consensus of tracking control problems is discussed by the Lyapunov function. The main purpose of this study is to design an adaptive control protocol for the system, such that even if there exists time delay among agents, the protocol can still ensure the consensus of the stochastic system. The main contribution is to revise the protocols that were previously only applicable to system without time delay. Because the system is inevitably disrupted by time delay and noise during the interactive process, achieving coordination and consensus is difficult. To enable the followers to track the leader, a novel adaptive law depending on the Riccati equation is firstly proposed, and the adaptive law is different from previous mandatory control law completely depending on a known function. The ability to be altered online based on the state of system is a major feature of the adaptive law. When there are interactive noise and time delay between the followers and leader of the system, a special Lyapunov function is constructed to prove the adaptive consensus. And the upper bound of time delay is obtained by using the Itô integral theory. Finally, if the time delay of the system approaches zero, it is shown that the adaptive law still ensures that each follower tracks the leader under simpler conditions.https://www.mdpi.com/2227-7390/11/16/3517time delaymulti-agent systemadaptive lawwhite noise |
| spellingShingle | Shoubo Jin Guanghui Zhang Adaptive Consensus of the Stochastic Leader-Following Multi-Agent System with Time Delay Mathematics time delay multi-agent system adaptive law white noise |
| title | Adaptive Consensus of the Stochastic Leader-Following Multi-Agent System with Time Delay |
| title_full | Adaptive Consensus of the Stochastic Leader-Following Multi-Agent System with Time Delay |
| title_fullStr | Adaptive Consensus of the Stochastic Leader-Following Multi-Agent System with Time Delay |
| title_full_unstemmed | Adaptive Consensus of the Stochastic Leader-Following Multi-Agent System with Time Delay |
| title_short | Adaptive Consensus of the Stochastic Leader-Following Multi-Agent System with Time Delay |
| title_sort | adaptive consensus of the stochastic leader following multi agent system with time delay |
| topic | time delay multi-agent system adaptive law white noise |
| url | https://www.mdpi.com/2227-7390/11/16/3517 |
| work_keys_str_mv | AT shoubojin adaptiveconsensusofthestochasticleaderfollowingmultiagentsystemwithtimedelay AT guanghuizhang adaptiveconsensusofthestochasticleaderfollowingmultiagentsystemwithtimedelay |