doi: 10.3934/dcdss.2022088
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

Bounded consensus of double-integrator stochastic multi-agent systems

1. 

Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China

2. 

Department of Mathematics, Guizhou Education University, Guiyang, Guizhou 550018, China

* Corresponding author: Jinrong Wang

Received  September 2021 Revised  February 2022 Early access April 2022

In the framework of fixed topology and stochastic switching topologies, we study the mean-square bounded consensus(MSBC) of double-integrator stochastic multi-agent systems(SMASs) including additive system noises and communication noises. Combining algebra, graph theory and random analysis, we obtain several equivalent conditions for double-integrator SMASs to reach MSBC. In addition, the simulation examples also verify the correctness of the theoretical results.

Citation: Mei Luo, Jinrong Wang, Yumei Liao. Bounded consensus of double-integrator stochastic multi-agent systems. Discrete and Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2022088
References:
[1]

J. W. Brewer, Kronecker products and matrix calculus in system theory. Special issue on the mathematical foundations of system theory, IEEE Trans. Circuits and Systems, 25 (1978), 772-781.  doi: 10.1109/TCS.1978.1084534.

[2]

X. K. CaoM. FečkanD. Shen and J. Wang, Iterative learning control for multi-agent systems with impulsive consensus tracking, Nonlinear Anal. Model. Control, 26 (2021), 130-150.  doi: 10.15388/namc.2021.26.20981.

[3]

B. B. Chang, X. W. Mu, Z. Yang and J. Y. Fang, Event-based secure consensus of muti-agent systems under asynchronous DoS attacks, Applied Mathematics and Computation, 401 (2021), 126120, 11 pp. doi: 10.1016/j.amc.2021.126120.

[4]

G. ChenL. Y. WangC. Chen and G. Yin, Critical connectivity and fastest convergence rates of distributed consensus with switching topologies and additive noises, IEEE Trans. Automat. Control, 62 (2017), 6152-6167.  doi: 10.1109/TAC.2017.2696824.

[5]

Z. Y. ChenY. LiuW. HeH. Qiao and H. Ji, Adaptive-neural-network-based trajectory tracking control for a nonholonomic wheeled mobile robot with velocity constraints, IEEE Transactions on Industrial Electronics, 68 (2021), 5057-5067.  doi: 10.1109/TIE.2020.2989711.

[6]

O. L. V. Costa and M. D. Fragoso, Stability results for discrete-time linear systems with Markovian jumping parameters, J. Math. Anal. Appl., 179 (1993), 154-178.  doi: 10.1006/jmaa.1993.1341.

[7]

D. R. DingZ. D. WangQ. L. Han and G. L. Wei, Security control for discrete-time stochastic nonlinear systems subject to deception attacks, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48 (2018), 779-789.  doi: 10.1109/TSMC.2016.2616544.

[8]

L. DingS. LiY.-J. LiuH. GaoC. Chao and Z. Deng, Adaptive neural network-based tracking control for full-state constrained wheeled mobile robotic system, IEEE Transactions on Systems Man Cybernetics: Systems, 47 (2017), 2410-2419.  doi: 10.1109/TSMC.2017.2677472.

[9]

T. Dong and Y. L. Gong, Leader-following secure consensus for second-order multi-agent systems with nonlinear dynamics and event-triggered control strategy under DoS attack, Neurocomputing, 416 (2020), 95-102.  doi: 10.1016/j.neucom.2019.01.113.

[10]

X. Q. FengY. C. Yang and D. X. Wei, Adaptive fully distributed consensus for a class of heterogeneous nonlinear multi-agent systems, Neurocomputing, 428 (2021), 12-18.  doi: 10.1016/j.neucom.2020.11.043.

[11]

M. D. Fragoso and O. L. V. Costa, A unified approach for stochastic and mean square stability of continuous-time linear systems with Markovian jumping parameters and additive disturbances, SIAM J. Control Optim., 44 (2005), 1165-1191.  doi: 10.1137/S0363012903434753.

[12]

R. Hou, L. Z. Cui, X. H. Bu and J. Q. Yang, Distributed formation control for multiple non-holonomic wheeled mobile robots with velocity constraint by using improved data-driven iterative learning, Applied Mathematics and Computation, 395 (2021), 125829, 15 pp. doi: 10.1016/j.amc.2020.125829.

[13]

N. HuangZ. S. Duan and Y. Zhao, Consensus of multi-agent systems via delayed and intermittent communications, IET Control Theory and Applications, 9 (2015), 62-73.  doi: 10.1049/iet-cta.2014.0729.

[14]

B.-Y. Kim and H.-S. Ahn, Distributed coordination and control for a freeway traffic network using consensus algorithms, IEEE Systems Journal, 10 (2016), 162-168.  doi: 10.1109/JSYST.2014.2318054.

[15]

M. L. Li and F. Q. Deng, Necessary and sufficient conditions for consensus of continuous-time multiagent systems with Markovian switching topologies and communication noises, IEEE Transactions on Cybernetics, 50 (2020), 3264-3270.  doi: 10.1109/TCYB.2019.2919740.

[16]

S. LiZ. LiJ. LiT. FernandoH. Ho-Ching IuQ. Wang and X. Liu, Application of event-triggered cubature Kalman filter for remote nonlinear state estimation in wireless sensor network, IEEE Transactions on Industrial Electronics, 68 (2021), 5133-5145.  doi: 10.1109/TIE.2020.2987279.

[17]

S. E. LiZ. WangY. ZhengD. Yang and K. You, Stability of general linear dynamic multi-agent systems under switching topologies with positive real eigenvalues, Engineering, 6 (2020), 688-694.  doi: 10.1016/j.eng.2020.05.006.

[18]

X. D. LiD. W. C. Ho and J. D. Cao, Finite-time stability and settling-time estimation of nonlinear impulsive systems, Automatica J. IFAC, 99 (2019), 361-368.  doi: 10.1016/j.automatica.2018.10.024.

[19]

X. D. Li and P. Li, Stability of time-delay systems with impulsive control involving stabilizing delays, Automatica J. IFAC, 124 (2021), 109336, 6 pp. doi: 10.1016/j.automatica.2020.109336.

[20]

X. D. LiD. X. Peng and J. D. Cao, Lyapunov stability for impulsive systems via event-triggered impulsive control, IEEE Transactions on Automatic Control, 65 (2020), 4908-4913.  doi: 10.1109/TAC.2020.2964558.

[21]

X. D. LiS. J. Song and J. H. Wu, Exponential stability of nonlinear systems with delayed impulses and applications, IEEE Transactions on Automatic Control, 64 (2019), 4024-4034.  doi: 10.1109/TAC.2019.2905271.

[22]

X. D. LiX. Y. Yang and S. J. Song, Lyapunov conditions for finite-time stability of time-varying time-delay systems, Automatica J. IFAC, 103 (2019), 135-140.  doi: 10.1016/j.automatica.2019.01.031.

[23]

X. D. Li, X. Y. Yang and J. D. Cao, Event-triggered impulsive control for nonlinear delay systems, Automatica J. IFAC, 117 (2020), 108981, 7 pp. doi: 10.1016/j.automatica.2020.108981.

[24]

X. D. LiH. T. Zhu and S. J. Song, Input-to-state stability of nonlinear systems using observer-based event-triggered impulsive control, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51 (2021), 6892-6900.  doi: 10.1109/TSMC.2020.2964172.

[25]

Z. Y. Li and Y. G. Liu, Consensus of vehicle platoon with the hidden layer against stochastic noise, Proceedings of the 38th Chinese Control Conference, (2019). doi: 10.23919/ChiCC.2019.8865730.

[26]

C. Y. LiuX. Q. WuX. X. Wan and J. H. Lu, Time-varying output formation tracking of heterogeneous linear multi-agent systems with dynamical controllers, Neurocomputing, 441 (2021), 36-43.  doi: 10.1016/j.neucom.2021.01.113.

[27]

J. LiuQ. Shao and C. C. Hua, Consensus-based cubature information filtering for sensor networks with incomplete measurements, Neurocomputing, 364 (2019), 49-62.  doi: 10.1016/j.neucom.2019.07.030.

[28]

D. LuoJ. Wang and D. Shen, Consensus tracking problem for linear fractional multi-agent systems with initial state error, Nonlinear Anal. Model. Control, 25 (2020), 766-785.  doi: 10.15388/namc.2020.25.18128.

[29]

D. LuoJ. Wang and D. Shen, $PD^{\alpha}$-type distributed learning control for nonlinear fractional-order multi-agent systems, Math. Methods Appl. Sci., 42 (2019), 4543-4553.  doi: 10.1002/mma.5677.

[30]

D. LuoJ. Wang and D. Shen, Learning formation control for fractional-order multiagent systems, Math. Methods Appl. Sci., 41 (2018), 5003-5014.  doi: 10.1002/mma.4948.

[31]

X. Mao, Stochastic Differential Equations and Application, Second edition, Horwood Publishing Limited, Chichester, 2008. doi: 10.1533/9780857099402.

[32]

S. X. Miao and H. S. Su, Second-order consensus of multiagent systems with matrix-weighted network, Neurocomputing, 433 (2021), 1-9.  doi: 10.1016/j.neucom.2020.12.056.

[33]

N. K. MuX. F. Liao and T. W. Huang, Consensus of second-order multi-agent systems with random sampling via event-triggered control, J. Franklin Inst., 353 (2016), 1423-1435.  doi: 10.1016/j.jfranklin.2016.01.014.

[34]

H. Neudecker, Some theorems on matrix differentiation with special reference to Kronecker matrix products, Journal of the American Statistical Association, 327 (2012), 953-963.  doi: 10.1080/01621459.1969.10501027.

[35]

H. Q. Pei and Q. Lai, Consensus of second-order multiagent systems with directed signed networks and communication delays, Complexity, 2020 (2020), 1712643, 10 pp. doi: 10.1155/2020/1712643.

[36]

W. Z. Qiu and J. Wang, Iterative learning control for multi-agent systems with noninstantaneous impulsive consensus tracking, Internat. J. Robust Nonlinear Control, 31 (2021), 6507-6524.  doi: 10.1002/rnc.5627.

[37]

W. Ren and E. Atkins, Distributed multi-vehicle coordinated control via local information exchange, Internat. J. Robust Nonlinear Control, 17 (2007), 1002-1033.  doi: 10.1002/rnc.1147.

[38]

M. Sader, Z. Q. Chen, Z. X. Liu and C. Deng, Distributed robust fault-tolerant consensus control for a class of nonlinear multi-agent systems with intermittent communications, Applied Mathematics and Computation, 403 (2021), 126166, 15 pp. doi: 10.1016/j.amc.2021.126166.

[39]

Y. ShangC. L. Liu and K. C. Cao, Event-triggered consensus control of nonlinear multi-agent systems based on first-order hold, International Journal of Control Automation and Systems, 19 (2021), 1461-1469.  doi: 10.1007/s12555-020-0145-y.

[40]

Y. C. Si and J. Wang, Relative controllability of multi-agent systems with pairwise different delays in states, Nonlinear Anal. Model. Control, 27 (2022), 289-307.  doi: 10.15388/namc.2022.27.25333.

[41]

F. L. SunC. Y. Lei and J. Kurths, Consensus of heterogeneous discrete-time multi-agent systems with noise over Markov switching topologies, Internat. J. Robust Nonlinear Control, 31 (2021), 1530-1541.  doi: 10.1002/rnc.5360.

[42]

H. Sun, Y. G. Liu and F. Z. Li, Distributed optimal consensus of second-order multi-agent systems, Science China-Information Sciences, 64 (2021), 209201, 3 pp. doi: 10.1007/s11432-018-9879-3.

[43]

S. S. TianY. X. LiY. L. Kang and J. N. Xia, Multi-robot path planning in wireless sensor networks based on jump mechanism PSO and safety gap obstacle avoidance, Future Generation Computer Systems-The International Journal of Escience, 118 (2021), 37-47.  doi: 10.1016/j.future.2020.12.012.

[44]

C. WangC. L. Liu and S. Liu, Robust fixed-time connectivity-preserving consensus for second-order multi-agent systems with external disturbances, IET Control Theory and Applications, 14 (2020), 2674-2681.  doi: 10.1049/iet-cta.2019.1487.

[45]

C. Y. WangH. TnunayZ. ZuoB. Lennox and Z. Ding, Fixed-time formation control of multirobot systems: Design and experiments, IEEE Transactions on Industrial Electronics, 66 (2019), 6292-6301.  doi: 10.1109/TIE.2018.2870409.

[46]

M. Wang and T. Zhang, Leader-following formation control of second-order nonlinear systems with time-varying communication delay, International Journal of Control Automation and Systems, 19 (2021), 1729-1739.  doi: 10.1007/s12555-019-0759-0.

[47]

Z. M. WangH. F. SunH. S. Zhang and X. Y. Liu, Bounded consensus control for stochastic multi-agent systems with additive noises, Neurocomputing, 408 (2020), 72-79.  doi: 10.1016/j.neucom.2019.11.027.

[48]

T. D. WeiX. Xie and X. D. Li, Persistence and periodicity of survival red blood cells model with time-varying delays and impulses, Mathematical Modelling and Control, 1 (2021), 12-25.  doi: 10.3934/mmc.2021002.

[49]

C. K. WongC. Cai and B. G. Heydecker, Adaptive traffic signal control using approximate dynamic programming, Transportation Research Part C: Emerging Technologies, 17 (2009), 456-474.  doi: 10.1016/j.trc.2009.04.005.

[50]

S. T. Yang and B. Yang, A semi-decentralized feudal multi-agent learned-goal algorithm for multi-intersection traffic signal control, Knowledge-Based Systems, 213 (2021), 106708, 15 pp. doi: 10.1016/j.knosys.2020.106708.

[51]

Y. YangY. F. LiD. YueY. C. Tian and X. H. Ding, Distributed secure consensus control with event-triggering for multiagent systems under DoS attacks, IEEE Transactions on Cybernetics, 51 (2021), 2916-2928.  doi: 10.1109/TCYB.2020.2979342.

[52]

K. Y. YouZ. K. Li and L. H. Xie, Consensus condition for linear multi-agent systems over randomly switching topologies, Automatica, 49 (2013), 3125-3132.  doi: 10.1016/j.automatica.2013.07.024.

[53]

S. YuanC. P. Yu and J. Sun, Adaptive event-triggered consensus control of linear multi-agent systems with cyber attacks, Neurocomputing, 442 (2021), 1-9.  doi: 10.1016/j.neucom.2021.02.040.

[54]

H. ZhangX. ZhouH. Yan and J. Sun, Adaptive consensus-based distributed target tracking with dynamic cluster in sensor networks, IEEE Transactions on Cybernetics, 49 (2019), 1580-1591.  doi: 10.1109/TCYB.2018.2805717.

[55]

J. ZhangH. G. ZhangY. L. Cai and W. H. Li, Containment control of general linear multi-agent systems by event-triggered control mechanisms, Neurocomputing, 433 (2021), 263-274.  doi: 10.1016/j.neucom.2020.11.008.

[56]

Y. Zhang and Y. P. Tian, Consentability and protocol design of multi agent systems with stochastic switching topology, Automatica J. IFAC, 45 (2009), 1195-1201.  doi: 10.1016/j.automatica.2008.11.005.

[57]

Y. Y. ZhangR. F. Li and X. M. Huo, Stochastic consensus of discrete-time second-order multi-agent systems with measurement noises and time delays, Journal of the Franklin Institute, 355 (2018), 2791-2807.  doi: 10.1016/j.jfranklin.2018.01.015.

[58]

X. F. ZongT. Li and J. F. Zhang, Consensus conditions of continuous-time multi-agent systems with additive and multiplicative measurement noises, SIAM Journal on Control and Optimization, 56 (2018), 19-52.  doi: 10.1137/15M1019775.

[59]

X. F. ZongT. Li and J. F. Zhang, Consensus of nonlinear multi-agent systems with multiplicative noises and time-varying delays, IEEE Conference on Decision and Control, (2018), 5415-5420.  doi: 10.1109/CDC.2018.8618969.

show all references

References:
[1]

J. W. Brewer, Kronecker products and matrix calculus in system theory. Special issue on the mathematical foundations of system theory, IEEE Trans. Circuits and Systems, 25 (1978), 772-781.  doi: 10.1109/TCS.1978.1084534.

[2]

X. K. CaoM. FečkanD. Shen and J. Wang, Iterative learning control for multi-agent systems with impulsive consensus tracking, Nonlinear Anal. Model. Control, 26 (2021), 130-150.  doi: 10.15388/namc.2021.26.20981.

[3]

B. B. Chang, X. W. Mu, Z. Yang and J. Y. Fang, Event-based secure consensus of muti-agent systems under asynchronous DoS attacks, Applied Mathematics and Computation, 401 (2021), 126120, 11 pp. doi: 10.1016/j.amc.2021.126120.

[4]

G. ChenL. Y. WangC. Chen and G. Yin, Critical connectivity and fastest convergence rates of distributed consensus with switching topologies and additive noises, IEEE Trans. Automat. Control, 62 (2017), 6152-6167.  doi: 10.1109/TAC.2017.2696824.

[5]

Z. Y. ChenY. LiuW. HeH. Qiao and H. Ji, Adaptive-neural-network-based trajectory tracking control for a nonholonomic wheeled mobile robot with velocity constraints, IEEE Transactions on Industrial Electronics, 68 (2021), 5057-5067.  doi: 10.1109/TIE.2020.2989711.

[6]

O. L. V. Costa and M. D. Fragoso, Stability results for discrete-time linear systems with Markovian jumping parameters, J. Math. Anal. Appl., 179 (1993), 154-178.  doi: 10.1006/jmaa.1993.1341.

[7]

D. R. DingZ. D. WangQ. L. Han and G. L. Wei, Security control for discrete-time stochastic nonlinear systems subject to deception attacks, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48 (2018), 779-789.  doi: 10.1109/TSMC.2016.2616544.

[8]

L. DingS. LiY.-J. LiuH. GaoC. Chao and Z. Deng, Adaptive neural network-based tracking control for full-state constrained wheeled mobile robotic system, IEEE Transactions on Systems Man Cybernetics: Systems, 47 (2017), 2410-2419.  doi: 10.1109/TSMC.2017.2677472.

[9]

T. Dong and Y. L. Gong, Leader-following secure consensus for second-order multi-agent systems with nonlinear dynamics and event-triggered control strategy under DoS attack, Neurocomputing, 416 (2020), 95-102.  doi: 10.1016/j.neucom.2019.01.113.

[10]

X. Q. FengY. C. Yang and D. X. Wei, Adaptive fully distributed consensus for a class of heterogeneous nonlinear multi-agent systems, Neurocomputing, 428 (2021), 12-18.  doi: 10.1016/j.neucom.2020.11.043.

[11]

M. D. Fragoso and O. L. V. Costa, A unified approach for stochastic and mean square stability of continuous-time linear systems with Markovian jumping parameters and additive disturbances, SIAM J. Control Optim., 44 (2005), 1165-1191.  doi: 10.1137/S0363012903434753.

[12]

R. Hou, L. Z. Cui, X. H. Bu and J. Q. Yang, Distributed formation control for multiple non-holonomic wheeled mobile robots with velocity constraint by using improved data-driven iterative learning, Applied Mathematics and Computation, 395 (2021), 125829, 15 pp. doi: 10.1016/j.amc.2020.125829.

[13]

N. HuangZ. S. Duan and Y. Zhao, Consensus of multi-agent systems via delayed and intermittent communications, IET Control Theory and Applications, 9 (2015), 62-73.  doi: 10.1049/iet-cta.2014.0729.

[14]

B.-Y. Kim and H.-S. Ahn, Distributed coordination and control for a freeway traffic network using consensus algorithms, IEEE Systems Journal, 10 (2016), 162-168.  doi: 10.1109/JSYST.2014.2318054.

[15]

M. L. Li and F. Q. Deng, Necessary and sufficient conditions for consensus of continuous-time multiagent systems with Markovian switching topologies and communication noises, IEEE Transactions on Cybernetics, 50 (2020), 3264-3270.  doi: 10.1109/TCYB.2019.2919740.

[16]

S. LiZ. LiJ. LiT. FernandoH. Ho-Ching IuQ. Wang and X. Liu, Application of event-triggered cubature Kalman filter for remote nonlinear state estimation in wireless sensor network, IEEE Transactions on Industrial Electronics, 68 (2021), 5133-5145.  doi: 10.1109/TIE.2020.2987279.

[17]

S. E. LiZ. WangY. ZhengD. Yang and K. You, Stability of general linear dynamic multi-agent systems under switching topologies with positive real eigenvalues, Engineering, 6 (2020), 688-694.  doi: 10.1016/j.eng.2020.05.006.

[18]

X. D. LiD. W. C. Ho and J. D. Cao, Finite-time stability and settling-time estimation of nonlinear impulsive systems, Automatica J. IFAC, 99 (2019), 361-368.  doi: 10.1016/j.automatica.2018.10.024.

[19]

X. D. Li and P. Li, Stability of time-delay systems with impulsive control involving stabilizing delays, Automatica J. IFAC, 124 (2021), 109336, 6 pp. doi: 10.1016/j.automatica.2020.109336.

[20]

X. D. LiD. X. Peng and J. D. Cao, Lyapunov stability for impulsive systems via event-triggered impulsive control, IEEE Transactions on Automatic Control, 65 (2020), 4908-4913.  doi: 10.1109/TAC.2020.2964558.

[21]

X. D. LiS. J. Song and J. H. Wu, Exponential stability of nonlinear systems with delayed impulses and applications, IEEE Transactions on Automatic Control, 64 (2019), 4024-4034.  doi: 10.1109/TAC.2019.2905271.

[22]

X. D. LiX. Y. Yang and S. J. Song, Lyapunov conditions for finite-time stability of time-varying time-delay systems, Automatica J. IFAC, 103 (2019), 135-140.  doi: 10.1016/j.automatica.2019.01.031.

[23]

X. D. Li, X. Y. Yang and J. D. Cao, Event-triggered impulsive control for nonlinear delay systems, Automatica J. IFAC, 117 (2020), 108981, 7 pp. doi: 10.1016/j.automatica.2020.108981.

[24]

X. D. LiH. T. Zhu and S. J. Song, Input-to-state stability of nonlinear systems using observer-based event-triggered impulsive control, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51 (2021), 6892-6900.  doi: 10.1109/TSMC.2020.2964172.

[25]

Z. Y. Li and Y. G. Liu, Consensus of vehicle platoon with the hidden layer against stochastic noise, Proceedings of the 38th Chinese Control Conference, (2019). doi: 10.23919/ChiCC.2019.8865730.

[26]

C. Y. LiuX. Q. WuX. X. Wan and J. H. Lu, Time-varying output formation tracking of heterogeneous linear multi-agent systems with dynamical controllers, Neurocomputing, 441 (2021), 36-43.  doi: 10.1016/j.neucom.2021.01.113.

[27]

J. LiuQ. Shao and C. C. Hua, Consensus-based cubature information filtering for sensor networks with incomplete measurements, Neurocomputing, 364 (2019), 49-62.  doi: 10.1016/j.neucom.2019.07.030.

[28]

D. LuoJ. Wang and D. Shen, Consensus tracking problem for linear fractional multi-agent systems with initial state error, Nonlinear Anal. Model. Control, 25 (2020), 766-785.  doi: 10.15388/namc.2020.25.18128.

[29]

D. LuoJ. Wang and D. Shen, $PD^{\alpha}$-type distributed learning control for nonlinear fractional-order multi-agent systems, Math. Methods Appl. Sci., 42 (2019), 4543-4553.  doi: 10.1002/mma.5677.

[30]

D. LuoJ. Wang and D. Shen, Learning formation control for fractional-order multiagent systems, Math. Methods Appl. Sci., 41 (2018), 5003-5014.  doi: 10.1002/mma.4948.

[31]

X. Mao, Stochastic Differential Equations and Application, Second edition, Horwood Publishing Limited, Chichester, 2008. doi: 10.1533/9780857099402.

[32]

S. X. Miao and H. S. Su, Second-order consensus of multiagent systems with matrix-weighted network, Neurocomputing, 433 (2021), 1-9.  doi: 10.1016/j.neucom.2020.12.056.

[33]

N. K. MuX. F. Liao and T. W. Huang, Consensus of second-order multi-agent systems with random sampling via event-triggered control, J. Franklin Inst., 353 (2016), 1423-1435.  doi: 10.1016/j.jfranklin.2016.01.014.

[34]

H. Neudecker, Some theorems on matrix differentiation with special reference to Kronecker matrix products, Journal of the American Statistical Association, 327 (2012), 953-963.  doi: 10.1080/01621459.1969.10501027.

[35]

H. Q. Pei and Q. Lai, Consensus of second-order multiagent systems with directed signed networks and communication delays, Complexity, 2020 (2020), 1712643, 10 pp. doi: 10.1155/2020/1712643.

[36]

W. Z. Qiu and J. Wang, Iterative learning control for multi-agent systems with noninstantaneous impulsive consensus tracking, Internat. J. Robust Nonlinear Control, 31 (2021), 6507-6524.  doi: 10.1002/rnc.5627.

[37]

W. Ren and E. Atkins, Distributed multi-vehicle coordinated control via local information exchange, Internat. J. Robust Nonlinear Control, 17 (2007), 1002-1033.  doi: 10.1002/rnc.1147.

[38]

M. Sader, Z. Q. Chen, Z. X. Liu and C. Deng, Distributed robust fault-tolerant consensus control for a class of nonlinear multi-agent systems with intermittent communications, Applied Mathematics and Computation, 403 (2021), 126166, 15 pp. doi: 10.1016/j.amc.2021.126166.

[39]

Y. ShangC. L. Liu and K. C. Cao, Event-triggered consensus control of nonlinear multi-agent systems based on first-order hold, International Journal of Control Automation and Systems, 19 (2021), 1461-1469.  doi: 10.1007/s12555-020-0145-y.

[40]

Y. C. Si and J. Wang, Relative controllability of multi-agent systems with pairwise different delays in states, Nonlinear Anal. Model. Control, 27 (2022), 289-307.  doi: 10.15388/namc.2022.27.25333.

[41]

F. L. SunC. Y. Lei and J. Kurths, Consensus of heterogeneous discrete-time multi-agent systems with noise over Markov switching topologies, Internat. J. Robust Nonlinear Control, 31 (2021), 1530-1541.  doi: 10.1002/rnc.5360.

[42]

H. Sun, Y. G. Liu and F. Z. Li, Distributed optimal consensus of second-order multi-agent systems, Science China-Information Sciences, 64 (2021), 209201, 3 pp. doi: 10.1007/s11432-018-9879-3.

[43]

S. S. TianY. X. LiY. L. Kang and J. N. Xia, Multi-robot path planning in wireless sensor networks based on jump mechanism PSO and safety gap obstacle avoidance, Future Generation Computer Systems-The International Journal of Escience, 118 (2021), 37-47.  doi: 10.1016/j.future.2020.12.012.

[44]

C. WangC. L. Liu and S. Liu, Robust fixed-time connectivity-preserving consensus for second-order multi-agent systems with external disturbances, IET Control Theory and Applications, 14 (2020), 2674-2681.  doi: 10.1049/iet-cta.2019.1487.

[45]

C. Y. WangH. TnunayZ. ZuoB. Lennox and Z. Ding, Fixed-time formation control of multirobot systems: Design and experiments, IEEE Transactions on Industrial Electronics, 66 (2019), 6292-6301.  doi: 10.1109/TIE.2018.2870409.

[46]

M. Wang and T. Zhang, Leader-following formation control of second-order nonlinear systems with time-varying communication delay, International Journal of Control Automation and Systems, 19 (2021), 1729-1739.  doi: 10.1007/s12555-019-0759-0.

[47]

Z. M. WangH. F. SunH. S. Zhang and X. Y. Liu, Bounded consensus control for stochastic multi-agent systems with additive noises, Neurocomputing, 408 (2020), 72-79.  doi: 10.1016/j.neucom.2019.11.027.

[48]

T. D. WeiX. Xie and X. D. Li, Persistence and periodicity of survival red blood cells model with time-varying delays and impulses, Mathematical Modelling and Control, 1 (2021), 12-25.  doi: 10.3934/mmc.2021002.

[49]

C. K. WongC. Cai and B. G. Heydecker, Adaptive traffic signal control using approximate dynamic programming, Transportation Research Part C: Emerging Technologies, 17 (2009), 456-474.  doi: 10.1016/j.trc.2009.04.005.

[50]

S. T. Yang and B. Yang, A semi-decentralized feudal multi-agent learned-goal algorithm for multi-intersection traffic signal control, Knowledge-Based Systems, 213 (2021), 106708, 15 pp. doi: 10.1016/j.knosys.2020.106708.

[51]

Y. YangY. F. LiD. YueY. C. Tian and X. H. Ding, Distributed secure consensus control with event-triggering for multiagent systems under DoS attacks, IEEE Transactions on Cybernetics, 51 (2021), 2916-2928.  doi: 10.1109/TCYB.2020.2979342.

[52]

K. Y. YouZ. K. Li and L. H. Xie, Consensus condition for linear multi-agent systems over randomly switching topologies, Automatica, 49 (2013), 3125-3132.  doi: 10.1016/j.automatica.2013.07.024.

[53]

S. YuanC. P. Yu and J. Sun, Adaptive event-triggered consensus control of linear multi-agent systems with cyber attacks, Neurocomputing, 442 (2021), 1-9.  doi: 10.1016/j.neucom.2021.02.040.

[54]

H. ZhangX. ZhouH. Yan and J. Sun, Adaptive consensus-based distributed target tracking with dynamic cluster in sensor networks, IEEE Transactions on Cybernetics, 49 (2019), 1580-1591.  doi: 10.1109/TCYB.2018.2805717.

[55]

J. ZhangH. G. ZhangY. L. Cai and W. H. Li, Containment control of general linear multi-agent systems by event-triggered control mechanisms, Neurocomputing, 433 (2021), 263-274.  doi: 10.1016/j.neucom.2020.11.008.

[56]

Y. Zhang and Y. P. Tian, Consentability and protocol design of multi agent systems with stochastic switching topology, Automatica J. IFAC, 45 (2009), 1195-1201.  doi: 10.1016/j.automatica.2008.11.005.

[57]

Y. Y. ZhangR. F. Li and X. M. Huo, Stochastic consensus of discrete-time second-order multi-agent systems with measurement noises and time delays, Journal of the Franklin Institute, 355 (2018), 2791-2807.  doi: 10.1016/j.jfranklin.2018.01.015.

[58]

X. F. ZongT. Li and J. F. Zhang, Consensus conditions of continuous-time multi-agent systems with additive and multiplicative measurement noises, SIAM Journal on Control and Optimization, 56 (2018), 19-52.  doi: 10.1137/15M1019775.

[59]

X. F. ZongT. Li and J. F. Zhang, Consensus of nonlinear multi-agent systems with multiplicative noises and time-varying delays, IEEE Conference on Decision and Control, (2018), 5415-5420.  doi: 10.1109/CDC.2018.8618969.

Figure 1.  Topology $ \mathcal{G} $
Figure 2.  The state trajectories
Figure 3.  Network topology $ \{\mathcal{G}_{1}, \mathcal{G}_{2}, \mathcal{G}_{3}\} $
Figure 4.  The topological transformation diagram
Figure 5.  The state trajectories
Table 1.  The position of each agent
Agent 0 10 20 30 40 50
1 8 98.8028 126.8127 154.6091 179.8284 203.3477
2 2 80.8029 121.4406 153.7326 180.2018 204.0143
3 5 90.3149 124.2652 154.2146 180.1108 203.6502
4 4 87.0743 123.1808 153.3275 179.3758 203.0953
5 10 78.4122 120.9336 153.4453 180.1209 203.6704
6 6 93.0754 125.0095 153.7932 179.5006 202.9661
Agent 0 10 20 30 40 50
1 8 98.8028 126.8127 154.6091 179.8284 203.3477
2 2 80.8029 121.4406 153.7326 180.2018 204.0143
3 5 90.3149 124.2652 154.2146 180.1108 203.6502
4 4 87.0743 123.1808 153.3275 179.3758 203.0953
5 10 78.4122 120.9336 153.4453 180.1209 203.6704
6 6 93.0754 125.0095 153.7932 179.5006 202.9661
Table 2.  The velocity of each agent
Agent 0 10 20 30 40 50
1 80 2.4374 2.8897 2.8699 2.2523 2.6406
2 20 4.5277 3.5997 3.0241 2.2809 2.5409
3 50 3.3306 3.2226 2.9195 2.2264 2.5746
4 40 3.6902 3.3191 3.0047 2.2885 2.5710
5 10 4.8084 3.6863 2.9844 2.2629 2.5924
6 60 2.9621 3.0973 2.8919 2.2493 2.6171
Agent 0 10 20 30 40 50
1 80 2.4374 2.8897 2.8699 2.2523 2.6406
2 20 4.5277 3.5997 3.0241 2.2809 2.5409
3 50 3.3306 3.2226 2.9195 2.2264 2.5746
4 40 3.6902 3.3191 3.0047 2.2885 2.5710
5 10 4.8084 3.6863 2.9844 2.2629 2.5924
6 60 2.9621 3.0973 2.8919 2.2493 2.6171
Table 3.  The position of each agent
Agent 0 20 40 60 80 100 120
1 1 28.5681 50.5773 72.6362 94.7570 116.3468 138.3723
2 2 29.2191 50.7588 73.2699 95.6504 115.7632 138.0114
3 3 33.0884 49.7954 73.5687 96.0563 115.5744 137.8249
4 4 29.7302 50.4890 73.1723 95.2234 115.8630 138.2307
5 5 34.3277 48.9584 73.0675 94.9233 116.1680 138.3576
Agent 0 20 40 60 80 100 120
1 1 28.5681 50.5773 72.6362 94.7570 116.3468 138.3723
2 2 29.2191 50.7588 73.2699 95.6504 115.7632 138.0114
3 3 33.0884 49.7954 73.5687 96.0563 115.5744 137.8249
4 4 29.7302 50.4890 73.1723 95.2234 115.8630 138.2307
5 5 34.3277 48.9584 73.0675 94.9233 116.1680 138.3576
Table 4.  The velocity of each agent
Agent 0 20 40 60 80 100 120
1 6 1.1000 1.1000 1.1000 1.1000 1.1000 1.1000
2 5 0.9616 1.1125 1.1042 1.1115 1.1478 1.0758
3 2 0.4320 1.1781 1.1128 1.0867 1.1135 1.1100
4 4 0.7428 1.1314 1.1051 1.1116 1.1860 1.0625
5 0 0.2022 1.1915 1.1197 1.0935 1.1285 1.0718
Agent 0 20 40 60 80 100 120
1 6 1.1000 1.1000 1.1000 1.1000 1.1000 1.1000
2 5 0.9616 1.1125 1.1042 1.1115 1.1478 1.0758
3 2 0.4320 1.1781 1.1128 1.0867 1.1135 1.1100
4 4 0.7428 1.1314 1.1051 1.1116 1.1860 1.0625
5 0 0.2022 1.1915 1.1197 1.0935 1.1285 1.0718
[1]

Xiaojin Huang, Hongfu Yang, Jianhua Huang. Consensus stability analysis for stochastic multi-agent systems with multiplicative measurement noises and Markovian switching topologies. Numerical Algebra, Control and Optimization, 2022, 12 (3) : 601-610. doi: 10.3934/naco.2021024

[2]

Xi Zhu, Meixia Li, Chunfa Li. Consensus in discrete-time multi-agent systems with uncertain topologies and random delays governed by a Markov chain. Discrete and Continuous Dynamical Systems - B, 2020, 25 (12) : 4535-4551. doi: 10.3934/dcdsb.2020111

[3]

Nadia Loy, Andrea Tosin. Boltzmann-type equations for multi-agent systems with label switching. Kinetic and Related Models, 2021, 14 (5) : 867-894. doi: 10.3934/krm.2021027

[4]

Evelyn Buckwar, Girolama Notarangelo. A note on the analysis of asymptotic mean-square stability properties for systems of linear stochastic delay differential equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (6) : 1521-1531. doi: 10.3934/dcdsb.2013.18.1521

[5]

Bixiang Wang. Mean-square random invariant manifolds for stochastic differential equations. Discrete and Continuous Dynamical Systems, 2021, 41 (3) : 1449-1468. doi: 10.3934/dcds.2020324

[6]

Hailong Zhu, Jifeng Chu, Weinian Zhang. Mean-square almost automorphic solutions for stochastic differential equations with hyperbolicity. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 1935-1953. doi: 10.3934/dcds.2018078

[7]

Richard Carney, Monique Chyba, Chris Gray, George Wilkens, Corey Shanbrom. Multi-agent systems for quadcopters. Journal of Geometric Mechanics, 2022, 14 (1) : 1-28. doi: 10.3934/jgm.2021005

[8]

Rui Li, Yingjing Shi. Finite-time optimal consensus control for second-order multi-agent systems. Journal of Industrial and Management Optimization, 2014, 10 (3) : 929-943. doi: 10.3934/jimo.2014.10.929

[9]

Zhongkui Li, Zhisheng Duan, Guanrong Chen. Consensus of discrete-time linear multi-agent systems with observer-type protocols. Discrete and Continuous Dynamical Systems - B, 2011, 16 (2) : 489-505. doi: 10.3934/dcdsb.2011.16.489

[10]

Yibo Zhang, Jinfeng Gao, Jia Ren, Huijiao Wang. A type of new consensus protocol for two-dimension multi-agent systems. Numerical Algebra, Control and Optimization, 2017, 7 (3) : 345-357. doi: 10.3934/naco.2017022

[11]

Ke Yang, Wencheng Zou, Zhengrong Xiang, Ronghao Wang. Fully distributed consensus for higher-order nonlinear multi-agent systems with unmatched disturbances. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1535-1551. doi: 10.3934/dcdss.2020396

[12]

Chuchu Chen, Jialin Hong. Mean-square convergence of numerical approximations for a class of backward stochastic differential equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (8) : 2051-2067. doi: 10.3934/dcdsb.2013.18.2051

[13]

Fuke Wu, Peter E. Kloeden. Mean-square random attractors of stochastic delay differential equations with random delay. Discrete and Continuous Dynamical Systems - B, 2013, 18 (6) : 1715-1734. doi: 10.3934/dcdsb.2013.18.1715

[14]

Tyrone E. Duncan. Some partially observed multi-agent linear exponential quadratic stochastic differential games. Evolution Equations and Control Theory, 2018, 7 (4) : 587-597. doi: 10.3934/eect.2018028

[15]

Thai Son Doan, Martin Rasmussen, Peter E. Kloeden. The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor. Discrete and Continuous Dynamical Systems - B, 2015, 20 (3) : 875-887. doi: 10.3934/dcdsb.2015.20.875

[16]

Wenlian Lu, Fatihcan M. Atay, Jürgen Jost. Consensus and synchronization in discrete-time networks of multi-agents with stochastically switching topologies and time delays. Networks and Heterogeneous Media, 2011, 6 (2) : 329-349. doi: 10.3934/nhm.2011.6.329

[17]

Giulia Cavagnari, Antonio Marigonda, Benedetto Piccoli. Optimal synchronization problem for a multi-agent system. Networks and Heterogeneous Media, 2017, 12 (2) : 277-295. doi: 10.3934/nhm.2017012

[18]

Yilun Shang. Group pinning consensus under fixed and randomly switching topologies with acyclic partition. Networks and Heterogeneous Media, 2014, 9 (3) : 553-573. doi: 10.3934/nhm.2014.9.553

[19]

Zhiyong Sun, Toshiharu Sugie. Identification of Hessian matrix in distributed gradient-based multi-agent coordination control systems. Numerical Algebra, Control and Optimization, 2019, 9 (3) : 297-318. doi: 10.3934/naco.2019020

[20]

Hongru Ren, Shubo Li, Changxin Lu. Event-triggered adaptive fault-tolerant control for multi-agent systems with unknown disturbances. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1395-1414. doi: 10.3934/dcdss.2020379

2021 Impact Factor: 1.865

Metrics

  • PDF downloads (206)
  • HTML views (60)
  • Cited by (0)

Other articles
by authors

[Back to Top]