{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T16:48:34Z","timestamp":1764175714121,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,7]],"date-time":"2024-10-07T00:00:00Z","timestamp":1728259200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62006159","2020YFB1806405","20220810152104001","2022A1515011981","6024330003K"],"award-info":[{"award-number":["62006159","2020YFB1806405","20220810152104001","2022A1515011981","6024330003K"]}]},{"name":"National Key Research and Development Program","award":["62006159","2020YFB1806405","20220810152104001","2022A1515011981","6024330003K"],"award-info":[{"award-number":["62006159","2020YFB1806405","20220810152104001","2022A1515011981","6024330003K"]}]},{"name":"Shenzhen Natural Science Foundation","award":["62006159","2020YFB1806405","20220810152104001","2022A1515011981","6024330003K"],"award-info":[{"award-number":["62006159","2020YFB1806405","20220810152104001","2022A1515011981","6024330003K"]}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["62006159","2020YFB1806405","20220810152104001","2022A1515011981","6024330003K"],"award-info":[{"award-number":["62006159","2020YFB1806405","20220810152104001","2022A1515011981","6024330003K"]}]},{"name":"High-Level Talent Initiation Project of Shenzhen Polytechnic University","award":["62006159","2020YFB1806405","20220810152104001","2022A1515011981","6024330003K"],"award-info":[{"award-number":["62006159","2020YFB1806405","20220810152104001","2022A1515011981","6024330003K"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The consensus problem in stochastic multi-agent systems (MASs) with Markovian switching is addressed by proposing a novel distributed dynamic event-triggered (DDET) technique based on periodic sampling to reduce information transmission. Unlike traditional event-triggered control, the proposed periodic sampling-based DDET method is characterized by the following three advantages: (1) The need for continuous monitoring of the event trigger is eliminated. (2) Zeno behavior in stochastic MASs is effectively prevented. (3) Communication costs are significantly reduced. Based on this, sufficient conditions for achieving consensus in the mean-square sense are derived using Lyapunov\u2013Krasovskii functions, providing a solid theoretical foundation for the proposed strategy. The effectiveness of the proposed DDET control is validated through two numerical examples.<\/jats:p>","DOI":"10.3390\/axioms13100694","type":"journal-article","created":{"date-parts":[[2024,10,7]],"date-time":"2024-10-07T07:30:18Z","timestamp":1728286218000},"page":"694","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Consensus Control for Stochastic Multi-Agent Systems with Markovian Switching via Periodic Dynamic Event-Triggered Strategy"],"prefix":"10.3390","volume":"13","author":[{"given":"Xue","family":"Luo","sequence":"first","affiliation":[{"name":"School of Computing and Artificial Intelligence, Southwestern University of Finance and Economics, Chengdu 611130, China"}]},{"given":"Chengbo","family":"Yi","sequence":"additional","affiliation":[{"name":"School of Undergraduate Education, Shenzhen Ploytechnic University, Shenzhen 518055, China"}]},{"given":"Jianwen","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0703-0320","authenticated-orcid":false,"given":"Jingyi","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1765-8787","authenticated-orcid":false,"given":"Yi","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.physa.2017.08.094","article-title":"Modeling and simulation of dynamic ant colony\u2019s labor division for task allocation of UAV swarm","volume":"491","author":"Wu","year":"2018","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"129803","DOI":"10.1016\/j.physa.2024.129803","article-title":"Traffic flow impact of mixed heterogeneous platoons on highways: An approach combining driving simulation and microscopic traffic simulation","volume":"643","author":"Ren","year":"2024","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Fan, H., Chen, X., Shi, K., Liang, Y., Wang, Y., and Wen, H. (2024). Mittag-Leffler synchronization in finite time for uncertain fractional-order multi-delayed memristive neural networks with time-varying perturbations via information feedback. Fractal Fract., 8.","DOI":"10.3390\/fractalfract8070422"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"7126","DOI":"10.1109\/TCYB.2022.3192864","article-title":"Consensus of MASs with input and communication delays by predictor-based protocol","volume":"53","author":"Sun","year":"2022","journal-title":"IEEE Trans. Cybern."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1690","DOI":"10.1137\/23M1584678","article-title":"Distributed Global Consensus of LTI Mass with Heterogeneous Actuator Saturation and Communication Noises","volume":"62","author":"Wang","year":"2024","journal-title":"SIAM J. Control. Optim."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"109989","DOI":"10.1016\/j.automatica.2021.109989","article-title":"Reduced-order interval observer based consensus for MASs with time-varying interval uncertainties","volume":"135","author":"Wang","year":"2022","journal-title":"Automatica"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2015","DOI":"10.1109\/TAC.2023.3317505","article-title":"Event-Based Average Consensus of Disturbed MASs via Fully Distributed Sliding Mode Control","volume":"69","author":"Yao","year":"2024","journal-title":"IEEE Trans. Autom. Control."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1675","DOI":"10.1109\/TAC.2023.3326059","article-title":"Preset-time and preset-accuracy Human-in-the-Loop cluster consensus control for MASs under stochastic actuation attacks","volume":"69","author":"Liu","year":"2024","journal-title":"IEEE Trans. Autom. Control."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1109\/TCYB.2021.3119066","article-title":"Prescribed performance bipartite consensus control for stochastic nonlinear multiagent systems under event-triggered strategy","volume":"53","author":"Ren","year":"2023","journal-title":"IEEE Trans. Cybern."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"110871","DOI":"10.1016\/j.automatica.2023.110871","article-title":"Impulsive consensus of stochastic multi-agent systems under semi-Markovian switching topologies and application","volume":"150","author":"Hu","year":"2023","journal-title":"Automatica"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"127107","DOI":"10.1016\/j.physa.2022.127107","article-title":"Finite-time adaptive synchronization of coupled uncertain neural networks via intermittent control","volume":"596","author":"Zhou","year":"2022","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1997","DOI":"10.1002\/asjc.3320","article-title":"Leader-following consensus of nonlinear singular switched multi-agent systems via sliding mode control","volume":"26","author":"Cai","year":"2024","journal-title":"Asian J. Control."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/j.automatica.2017.04.006","article-title":"Distributed consensus tracking of a class of asynchronously switched nonlinear multi-agent systems","volume":"87","author":"Yoo","year":"2018","journal-title":"Automatica"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1109\/TFUZZ.2023.3302854","article-title":"Distributed event-triggered fuzzy control of heterogeneous switched multiagent systems under switching topologies","volume":"32","author":"Li","year":"2024","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"127969","DOI":"10.1016\/j.physa.2022.127969","article-title":"Group consensus of nonlinear multiagent system with switching topology under DoS attacks","volume":"605","author":"Xu","year":"2022","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"126589","DOI":"10.1016\/j.physa.2021.126589","article-title":"Output feedback control for bipartite consensus of nonlinear multi-agent systems with disturbances and switching topologies","volume":"589","author":"Parivallal","year":"2022","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2150","DOI":"10.1109\/TNSE.2022.3155405","article-title":"Tracking Consensus of Multi-Agent Systems Under Switching Topologies via Novel SMC: An Event-Triggered Approach","volume":"9","author":"Cai","year":"2022","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"115226","DOI":"10.1016\/j.chaos.2024.115226","article-title":"Distributed delayed impulsive control for \u03bc-synchronization of multi-link structure networks with bounded uncertainties and time-varying delays of unmeasured bounds: A novel Halanay impulsive inequality approach","volume":"186","author":"Fan","year":"2024","journal-title":"Chaos Solitons Fractals"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3173","DOI":"10.1109\/TSMC.2024.3357539","article-title":"Initial-value-free nonlinear mapping-based approach to practical finite\/fixed-time consensus control for constrained multiagent systems","volume":"54","author":"Wang","year":"2024","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"127289","DOI":"10.1016\/j.physa.2022.127289","article-title":"Adaptive size-independent control of uncertain leader following systems with only relative displacement information","volume":"597","author":"Chehardoli","year":"2022","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"128263","DOI":"10.1016\/j.physa.2022.128263","article-title":"Consensus in complex networks with noisy agents and peer pressure","volume":"608","author":"Griffin","year":"2022","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4592","DOI":"10.1109\/TSMC.2024.3380391","article-title":"Adaptive impulsive consensus of nonlinear multiagent systems with limited bandwidth under uncertain deception attacks","volume":"54","author":"Ren","year":"2024","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1109\/TSMC.2022.3166779","article-title":"Time cost for consensus of stochastic multiagent systems with pinning control","volume":"53","author":"Chang","year":"2023","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2240","DOI":"10.1109\/TCSI.2024.3350248","article-title":"Prespecified-time bipartite consensus of multi-agent systems via intermittent control","volume":"71","author":"Geng","year":"2024","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3524","DOI":"10.1109\/TAC.2016.2614486","article-title":"Event-triggered mean-square consensus control for time-varying stochastic multi-agent system with sensor saturations","volume":"62","author":"Ma","year":"2017","journal-title":"IEEE Trans. Autom. Control."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"110022","DOI":"10.1016\/j.automatica.2021.110022","article-title":"Event-triggered consensus control of continuous-time stochastic multi-agent systems","volume":"137","author":"Cao","year":"2022","journal-title":"Automatica"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"127586","DOI":"10.1016\/j.physa.2022.127586","article-title":"Bipartite synchronization of coupled delayed neural networks with cooperative-competitive interaction via event-triggered control","volume":"600","author":"Zhu","year":"2022","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"10314","DOI":"10.1109\/TCYB.2021.3070356","article-title":"Secure event-triggered consensus control of linear multiagent systems subject to sequential scaling attacks","volume":"52","author":"He","year":"2022","journal-title":"IEEE Trans. Cybern."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1109\/JAS.2023.123582","article-title":"Dynamic event-triggered consensus control for input constrained multi-agent systems with a designable minimum inter-event time","volume":"11","author":"Li","year":"2024","journal-title":"IEEE\/CAA J. Autom. Sin."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4581","DOI":"10.3934\/era.2024208","article-title":"Synchronization of a class of nonlinear multiple neural networks with delays via a dynamic event-triggered impulsive control strategy","volume":"32","author":"Yi","year":"2024","journal-title":"Electron. Res. Arch."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1489","DOI":"10.1016\/j.automatica.2014.03.017","article-title":"A distributed event-triggered transmission strategy for sampled-data consensus of multi-agent systems","volume":"50","author":"Guo","year":"2014","journal-title":"Automatica"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"109405","DOI":"10.1016\/j.automatica.2020.109405","article-title":"Event-triggered sliding mode control of networked control systems with Markovian jump parameters","volume":"125","author":"Su","year":"2021","journal-title":"Automatica"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1109\/TCSI.2020.3036847","article-title":"Adaptive event-triggered SMC for stochastic switching systems with Semi-Markov process and application to boost converter circuit model","volume":"68","author":"Qi","year":"2021","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"101091","DOI":"10.1016\/j.nahs.2021.101091","article-title":"Resilient self\/event-triggered consensus based on ternary control","volume":"42","author":"Matsume","year":"2021","journal-title":"Nonlinear Anal. Hybrid Syst."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Fan, H., Rao, Y., Shi, K., and Wen, H. (2024). Time-varying function matrix projection synchronization of Caputo fractional-order uncertain memristive neural networks with multiple delays via mixed open loop feedback control and impulsive control. Fractal Fract., 8.","DOI":"10.3390\/fractalfract8050301"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1016\/j.automatica.2012.11.013","article-title":"Modeling and adaptive tracking for a class of stochastic Lagrangian control systems","volume":"49","author":"Cui","year":"2013","journal-title":"Automatica"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Zhu, Y., Niu, B., Shang, Z., Wang, Z., and Wang, H. (2024). Distributed adaptive asymptotic consensus tracking control for stochastic nonlinear MASs with unknown control gains and output constraints. IEEE Trans. Autom. Sci. Eng., 1\u201311.","DOI":"10.1109\/TASE.2024.3350547"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.sysconle.2007.08.009","article-title":"Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays","volume":"57","author":"Sun","year":"2008","journal-title":"Syst. Control Lett."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"3469","DOI":"10.1007\/s11071-022-07999-y","article-title":"Almost sure consensus of stochastic nonlinear multi-agent systems via event-triggered control","volume":"111","author":"Yu","year":"2023","journal-title":"Nonlinear Dyn."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/j.ins.2018.04.054","article-title":"Event-triggered leader-following consensus for multi-agent systems with semi-Markov switching topologies","volume":"459","author":"Dai","year":"2018","journal-title":"Inf. Sci."},{"key":"ref_41","unstructured":"Oksendal, B. (2013). Stochastic Differential Equations: An Introduction with Applications, Springer Science and Business Media."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"3706","DOI":"10.1109\/ACCESS.2018.2790970","article-title":"Bipartite consensus control for coupled harmonic oscillators under a coopetitive network topology","volume":"6","author":"Liu","year":"2018","journal-title":"IEEE Access"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1109\/TSMC.2022.3189403","article-title":"The synchronization of networked harmonic oscillators under denial-of-service attacks","volume":"53","author":"Yang","year":"2023","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.isatra.2022.02.002","article-title":"Switching cluster synchronization control of networked harmonic oscillators subject to denial-of-service attacks","volume":"127","author":"Yang","year":"2022","journal-title":"ISA Trans."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/10\/694\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:12:04Z","timestamp":1760112724000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/10\/694"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,7]]},"references-count":44,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,10]]}},"alternative-id":["axioms13100694"],"URL":"https:\/\/doi.org\/10.3390\/axioms13100694","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2024,10,7]]}}}