Preset-Time Consensus of Heterogeneous Fractional-Order Nonlinear Multi-Agent Systems

GONG Ping

doi:10.21656/1000-0887.430223

Volume 44 Issue 5

May 2023

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2023 > 44(5): 605-618

GONG Ping. Preset-Time Consensus of Heterogeneous Fractional-Order Nonlinear Multi-Agent Systems[J]. Applied Mathematics and Mechanics, 2023, 44(5): 605-618. doi: 10.21656/1000-0887.430223

Citation:

GONG Ping. Preset-Time Consensus of Heterogeneous Fractional-Order Nonlinear Multi-Agent Systems[J]. Applied Mathematics and Mechanics, 2023, 44(5): 605-618. doi: 10.21656/1000-0887.430223

Citation:

GONG Ping. Preset-Time Consensus of Heterogeneous Fractional-Order Nonlinear Multi-Agent Systems[J]. Applied Mathematics and Mechanics, 2023, 44(5): 605-618. doi: 10.21656/1000-0887.430223

PDF( 1890 KB)

Preset-Time Consensus of Heterogeneous Fractional-Order Nonlinear Multi-Agent Systems

doi: 10.21656/1000-0887.430223

GONG Ping

School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, P.R.China

Received Date: 2022-07-04
Rev Recd Date: 2022-08-24
Publish Date: 2023-05-01

Abstract

Abstract

The preset-time consensus problem of a class of heterogeneous fractional-order nonlinear multi-agent systems was studied. A type of time-varying function-based preset-time fractional integral controllers were designed, to convert the fractional-order nonlinear multi-agent system into a 1st-order nonlinear multi-agent system. Then, by means of the integer-order Lyapunov function method combined with the preset-time control technology, the accurate bipartite consensus control of multi-agent systems with the connected undirected graph and the directed graph containing spanning trees was realized, respectively. The preset time can be preset with the time-varying function, independent of system initial values and parameters. An example verifies the effectiveness of the theoretical results.
- fractional-order multi-agent system,
- consensus problem,
- preset time,
- heterogeneous nonlinear dynamics

FullText(HTML)

References(35)

References

[1]	DU H, WEN G, CHENG Y, et al. Distributed finite-time cooperative control of multiple high-order nonholonomic mobile robots[J]. IEEE Transactions on Neural Networks and Learning Systems, 2017, 28(12): 2998-3006. doi: 10.1109/TNNLS.2016.2610140
[2]	DONG X, YU B, SHI Z, et al. Time-varying formation control for unmanned aerial vehicles: theories and applications[J]. IEEE Transactions Control System Technology, 2015, 23(1): 340-348. doi: 10.1109/TCST.2014.2314460
[3]	LESSER V, ORTIZ C L, TAMBE M. Distributed Sensor Networks: a Multiagent Perspective[M]. New York: Springer, 2003.
[4]	CHEN B, CHENG H. A review of the applications of agent technology in traffic and transportation systems[J]. IEEE Transactions on Intelligent Transportation Systems, 2010, 11(2): 485-497. doi: 10.1109/TITS.2010.2048313
[5]	GHARIB A, EJAZ W, IBNKAHLA M. Distributed spectrum sensing for IoT networks: architecture, challenges, and learning[J]. IEEE Internet of Things Magazine, 2021, 4(2): 66-73. doi: 10.1109/IOTM.0011.2000049
[6]	OLFATI-SABER R, M-MURRAY R. Consensus problems in networks of agents with switching topology and time-delays[J]. IEEE Transactions on Automatic Control, 2004, 49(9): 1520-1533. doi: 10.1109/TAC.2004.834113
[7]	郑丽颖, 杨永清, 许先云. 基于时变拓扑结构的二阶多智能体系统采样一致性[J]. 应用数学和力学, 2022, 43(7): 783-791. doi: 10.21656/1000-0887.420220 ZHENG Liying, YANG Yongqing, XU Xianyun. Sampling consensus of 2nd-order multi-agent systems based on time-varying topology[J]. Applied Mathematics and Mechanics, 2022, 43(7): 783-791. (in Chinese) doi: 10.21656/1000-0887.420220
[8]	QIN J, MA Q, SHI Y, et al. Recent advances in consensus of multi-agent systems: a brief survey[J]. IEEE Transactions on Industrial Electronics, 2016, 64(6): 4972-4983. http://www.researchgate.net/profile/Jiahu_Qin/publication/311505964_Recent_Advances_in_Consensus_of_Multi-Agent_Systems_A_Brief_Survey/links/5849797c08ae5038263d84cf/Recent-Advances-in-Consensus-of-Multi-Agent-Systems-A-Brief-Survey.pdf
[9]	ZUO Z, HAN Q L, NING B, et al. An overview of recent advances in fixed-time cooperative control of multiagent systems[J]. IEEE Transactions on Industrial Informatics, 2018, 14(6): 2322-2334. doi: 10.1109/TII.2018.2817248
[10]	KILBAS A A, SRIVASTAVA H M, TRUJILLO J J. Theory and Applications of Fractional Differential Equations[M]. Amsterdam: Elsevier Science, 2006.
[11]	Podlubny I. Fractional Differential Equations, Mathematics in Science and Engineering[M]. San Diego: Academic Press, 1999.
[12]	CAO Y C, LI Y, REN W, et al. Distributed coordination of networked fractional-order systems[J]. IEEE Transactions on Systems, Man, and Cybernetics(Part B): Cybernetics, 2009, 40(2): 362-370. http://www.researchgate.net/profile/YangQuan_Chen/publication/224560386_Distributed_Coordination_of_Networked_Fractional-Order_Systems/links/09e4150aa797b58580000000
[13]	GONG P, HAN Q L. Practical fixed-time bipartite consensus of nonlinear incommensurate fractional-order multiagent systems in directed signed networks[J]. SIAM Journal on Control and Optimization, 2020, 58(6): 3322-3341. doi: 10.1137/19M1282970
[14]	ZHU W, LI W, ZHOU P, et al. Consensus of fractional-order multi-agent systems with linear models via observer-type protocol[J]. Neurocomputing, 2017, 230: 60-65. doi: 10.1016/j.neucom.2016.11.052
[15]	CHEN J, CHEN B, ZENG Z. Synchronization and consensus in networks of linear fractional-order multi-agent systems via sampled-data control[J]. IEEE Transactions on Neural Networks and Learning Systems, 2019, 31(8): 2955-2964. http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8826011
[16]	LIU H, CHENG L, TAN M, et al. Exponential finite-time consensus of fractional-order multiagent systems[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2020, 50(4): 1549-1558. doi: 10.1109/TSMC.2018.2816060
[17]	SU H, YE Y, CHEN X, et al. Necessary and sufficient conditions for consensus in fractional-order multiagent systems via sampled data over directed graph[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(4): 2501-2511. doi: 10.1109/TSMC.2019.2915653
[18]	HU W, WEN G, RAHMANI A, et al. Differential evolution-based parameter estimation and synchronization of heterogeneous uncertain nonlinear delayed fractional-order multi-agent systems with unknown leader[J]. Nonlinear Dynamics, 2019, 97(2): 1087-1105. doi: 10.1007/s11071-019-05034-1
[19]	GONG P. Distributed tracking of heterogeneous nonlinear fractional-order multi-agent systems with an unknown leader[J]. Journal of the Franklin Institute, 2017, 354(5): 2226-2244. doi: 10.1016/j.jfranklin.2017.01.001
[20]	GONG P, LAN W. Adaptive robust tracking control for uncertain nonlinear fractional-order multi-agent systems with directed topologies[J]. Automatica, 2018, 92: 92-99. doi: 10.1016/j.automatica.2018.02.010
[21]	GONG P, HAN Q L, LAN W. Finite-time consensus tracking for incommensurate fractional-order nonlinear multiagent systems with directed switching topologies[J]. IEEE Transactions on Cybernetics, 2022, 52(1): 65-76. doi: 10.1109/TCYB.2020.2977169
[22]	马丽新, 刘晨, 刘磊. 基于actor-critic算法的分数阶多自主体系统最优主-从一致性控制[J]. 应用数学和力学, 2022, 43(1): 104-114. doi: 10.21656/1000-0887.420124 MA Lixin, LIU Chen, LIU Lei. Optimal leader-following consensus control of fractional-order multi-agent systems based on the actor-critic algorithm[J]. Applied Mathematics and Mechanics, 2022, 43(1): 104-114. (in Chinese) doi: 10.21656/1000-0887.420124
[23]	POLYAKOV A. Nonlinear feedback design for fixed-time stabilization of linear control systems[J]. IEEE Transactions on Automatic Control, 2012, 57(8): 2106-2110. doi: 10.1109/TAC.2011.2179869
[24]	SHI X, LU J, LIU Y, et al. A new class of fixed-time bipartite consensus protocols for multi-agent systems with antagonistic interactions[J]. Journal of Franklin Institute, 2018, 355(12): 5256-5271. doi: 10.1016/j.jfranklin.2018.05.006
[25]	ZOU W, QIAN K, XIANG Z. Fixed-time consensus for a class of heterogeneous nonlinear multiagent systems[J]. IEEE Transactions on Circuits and Systems: Express Briefs, 2020, 67(7): 1279-1283. doi: 10.1109/TCSII.2019.2930648
[26]	WANG H, YU W, WEN G, et al. Fixed-time consensus of nonlinear multi-agent systems with general directed topologies[J]. IEEE Transactions on Circuits and Systems : Express Briefs, 2019, 66(9): 1587-1591. doi: 10.1109/TCSII.2018.2886298
[27]	FU J, WANG J. Fixed-time coordinated tracking for second-order multi-agent systems with bounded input uncertainties[J]. Systems and Control Letters, 2016, 93: 1-12. doi: 10.1016/j.sysconle.2016.03.006
[28]	ZUO Z, TIAN B, DEFOORT M, et al. Fixed-time consensus tracking for multiagent systems with high-order integrator dynamics[J]. IEEE Transactions on Automatics Control, 2018, 63(2): 563-570. doi: 10.1109/TAC.2017.2729502
[29]	赵玮, 任凤丽. 基于牵制控制的多智能体系统的有限时间与固定时间一致性[J]. 应用数学和力学, 2021, 42(3): 299-307. doi: 10.21656/1000-0887.410190 ZHAO Wei, REN Fengli. Finite-time and fixed-time consensus for multi-agent systems via pinning control[J]. Applied Mathematics and Mechanics, 2021, 42(3): 299-307. (in Chinese) doi: 10.21656/1000-0887.410190
[30]	GONG P, HAN Q L. Fixed-time bipartite consensus tracking of fractional-order multi-agent systems with a dynamic leader[J]. IEEE Transactions on Circuits and Systems : Express Briefs, 2020, 67(10): 2054-2058. doi: 10.1109/TCSII.2019.2947353
[31]	BECERRA H M, VÁZQUEZ C R, ARECHAVALETA G, et al. Predefined-time convergence control for high-order integrator systems using time base generators[J]. IEEE Transactions on Control Systems Technology, 2018, 26(5): 1866-1873. doi: 10.1109/TCST.2017.2734050
[32]	NING B, HAN Q L, ZUO Z. Bipartite consensus tracking for second-order multiagent systems: a time-varying function-based preset-time approach[J]. IEEE Transactions on Automatics Control, 2021, 66(6): 2739-2745. doi: 10.1109/TAC.2020.3008125
[33]	WANG Y, SONG Y, HILL D J, et al. Prescribed-time consensus and containment control of networked multiagent systems[J]. IEEE Transactions on Cybernetics, 2019, 49(4): 1138-1147. doi: 10.1109/TCYB.2017.2788874
[34]	ZHOU Y, LI C, JIANG G P, et al. Robust prescribed-time consensus of multi-agent systems with actuator saturation and actuator faults[J]. Asian Journal of Control, 2022, 24(2): 743-754. doi: 10.1002/asjc.2625
[35]	LIU W, ZHOU S, QI Y, et al. Leaderless consensus of multiagent systems with Lipschitz nonlinear dynamics and switching topologies[J]. Neurocomputing, 2016, 173 : 1322-1329. http://www.onacademic.com/detail/journal_1000038285421810_abcf.html