April  2021, 14(4): 1535-1551. doi: 10.3934/dcdss.2020396

Fully distributed consensus for higher-order nonlinear multi-agent systems with unmatched disturbances

1. 

School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China

2. 

National Defense Engineering College, Army Engineering University, Nanjing 210007, China

* Corresponding author: Zhengrong Xiang

Received  October 2019 Revised  April 2020 Published  June 2020

Fund Project: This work was supported by the National Natural Science Foundation of China number 61873128 and 61603414

In this paper, the distributed consensus problem is investigated for a class of higher-order nonlinear multi-agent systems with unmatched disturbances. By the back-stepping technique, a new distributed protocol is designed to solve the consensus problem for multi-agent systems without using the information of the Laplacian matrix and Lipschitz constants. It is proved that the practical consensus of multi-agent systems with unmatched disturbances can be achieved by the proposed protocol. Finally, the validity of the proposed scheme is verified by a simulation.

Citation: Ke Yang, Wencheng Zou, Zhengrong Xiang, Ronghao Wang. Fully distributed consensus for higher-order nonlinear multi-agent systems with unmatched disturbances. Discrete & Continuous Dynamical Systems - S, 2021, 14 (4) : 1535-1551. doi: 10.3934/dcdss.2020396
References:
[1]

H. B. DuY. G. He and Y. Y. Cheng, Finite-time synchronization of a class of second-order nonlinear multi-agent systems using output feedback control, IEEE Transactions on Circuits and Systems I: Regular Papers, 61 (2014), 1778-1788.  doi: 10.1109/TCSI.2013.2295012.  Google Scholar

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K. FathianT. H. Summers and N. R. Gans, Robust distributed formation control of agents with higher-order dynamics, IEEE Control Systems Letters, 2 (2018), 495-500.  doi: 10.1109/LCSYS.2018.2841941.  Google Scholar

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L. Gao, J. Li, X. Zhu and W. Chen, Leader-following consensus of linear multi-agent systems with state-observer under switching topologies, 2012 12th International Conference on Control Automation Robotics and Vision, (2012), 572–577. Google Scholar

[6]

G. X. GuL. Marinovici and F. L. Lewis, Consensusability of discrete-time dynamic multiagent systems, IEEE Transactions on Automatic Control, 57 (2012), 2085-2089.  doi: 10.1109/TAC.2011.2179431.  Google Scholar

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G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge University Press, 1952.  Google Scholar

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[11]

Z. K. LiZ. S. Duan and F. L. Lewis, Distributed robust consensus control of multi-agent systems with heterogeneous matching uncertainties, Automatica J. IFAC, 50 (2014), 883-889.  doi: 10.1016/j.automatica.2013.12.008.  Google Scholar

[12]

H. Q. LiX. F. LiaoT. W. HuangW. Zhu and Y. B. Liu, Second-order global consensus in multiagent networks with random directional link failure, IEEE Transactions on Neural Networks and Learning Systems, 26 (2015), 565-575.  doi: 10.1109/TNNLS.2014.2320274.  Google Scholar

[13]

G. P. LiX. Y. Wang and S. H. Li, Finite-time output consensus of higher-order multiagent systems with mismatched disturbances and unknown state elements, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49 (2019), 2751-2581.  doi: 10.1109/TSMC.2017.2759095.  Google Scholar

[14]

G. P. LiX. Y. Wang and S. H. Li, Distributed composite output consensus protocols of higher-order multi-agent systems subject to mismatched disturbances, IET Control Theory and Applications, 11 (2017), 1162-1172.  doi: 10.1049/iet-cta.2016.0814.  Google Scholar

[15]

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[16]

C.-L. LiuL. ShanY.-Y. Chen and Y. Zhang, Average-consensus filter of first-order multi-agent systems with disturbances, IEEE Transactions on Circuits and Systems II: Express Briefs, 65 (2018), 1763-1767.  doi: 10.1109/TCSII.2017.2762723.  Google Scholar

[17]

C. Q. MaT. Li and J. F. Zhang, Consensus control for leader-following multi-agent systems with measurement noise, Journal of Systems Science and Complexity, 23 (2010), 35-49.  doi: 10.1007/s11424-010-9273-4.  Google Scholar

[18]

Z. Y. MengW. Ren and Z. You, Distributed finite-time attitude containment control for multiple rigid bodies, Autonmatica, 46 (2010), 2092-2099.  doi: 10.1016/j.automatica.2010.09.005.  Google Scholar

[19]

S. Mondal and R. Su, Disturbance observer based consensus control for higher order multi-agent systems with mismatched uncertainties, 2016 American Control Conference, (2016), 2826–2831. doi: 10.1109/ACC.2016.7525347.  Google Scholar

[20]

C. PengJ. Zhang and Q.-L. Han, Consensus of multiagent systems with nonlinear dynamics using an integrated sampled-data-based event-triggered communication scheme, IEEE Transactions on Systems, Man and Cybernetics: Systems, 49 (2019), 589-599.  doi: 10.1109/TSMC.2018.2814572.  Google Scholar

[21]

Z. R. QiuL. H. Xie and Y. G. Hong, Quantized leaderless and leader-following consensus of high-order multi-agent systems with limited data rate, IEEE Transactions on Automatic Control, 61 (2016), 2432-2447.  doi: 10.1109/TAC.2015.2495579.  Google Scholar

[22]

M. RehanA. Jameel and C. K. Ahn, Distributed consensus control of one-sided Lipschitz nonlinear multiagent systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48 (2018), 1297-1308.  doi: 10.1109/TSMC.2017.2667701.  Google Scholar

[23]

W. Ren and E. Atkins, Distributed multi-agent systems under dynamically changing interaction topologies, IEEE Transactions on Automatic Control, 50 (2005), 655-661.   Google Scholar

[24]

C. RenZ. Shi and T. Du, Distributed observer-based leader-following consensus control for second-order stochastic multi-agent systems, IEEE Access, 6 (2018), 20077-20084.  doi: 10.1109/ACCESS.2018.2820813.  Google Scholar

[25]

L. N. RongJ. W. LuS. Y. Xu and Y. M. Chu, Reference model-based containment control of multi-agent systems with higher-order dynamics, IET Control Theory and Applications, 8 (2014), 796-802.  doi: 10.1049/iet-cta.2013.0148.  Google Scholar

[26]

P. Shi and Q. Shen, Cooperative control of multi-agent systems with unknown state-dependent controlling effects, IEEE Transactions on Automation Science and Engineering, 12 (2015), 827-834.   Google Scholar

[27]

S. Z. Su and Z. L. Lin, Distributed synchronization control of multi-agent systems with switching directed communication topologies and unknown nonlinearities, 2015 54th IEEE Conference on Decision and Control, (2015), 5444–5449. doi: 10.1109/CDC.2015.7403072.  Google Scholar

[28]

X. H. WangY. G. Hong and H. B. Ji, Distributed optimization for a class of nonlinear multiagent systems with disturbance rejection, IEEE Transactions on Cybernetics, 46 (2016), 1655-1666.  doi: 10.1109/TCYB.2015.2453167.  Google Scholar

[29]

X. Y. WangS. H. LiX. H. Yu and J. Yang, Distributed active anti-disturbance consensus for leader-follower higher-order multi-agent systems with mismatched disturbances, IEEE Transactions on Automatic Control, 62 (2017), 5795-5801.  doi: 10.1109/TAC.2016.2638966.  Google Scholar

[30]

J. H. WangY. L. XuY. Xu and D. D. Yang, Time-varying formation for high-order multi-agent systems with external disturbances by event-triggered integral sliding mode control, Appl. Math. Comput., 359 (2019), 333-343.  doi: 10.1016/j.amc.2019.04.066.  Google Scholar

[31]

Z. WuY. XuY. PanP. Shi and Q. Wang, Event-triggered pinning control for consensus of multiagent systems with quantized information, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48 (2018), 1929-1938.   Google Scholar

[32]

D. YangX. D. Li and J. L. Qiu, Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback, Nonlinear Analysis: Hybrid Systems, 32 (2019), 294-305.  doi: 10.1016/j.nahs.2019.01.006.  Google Scholar

[33]

Z. Y. YuH. J. Jiang and C. Hu, Leader-following consensus of fractional-order multi-agent systems under fixed topology, Neurocomputing, 149 (2015), 613-620.  doi: 10.1016/j.neucom.2014.08.013.  Google Scholar

[34]

C. Zhang, Distributed ESO based cooperative tracking control for high-order nonlinear multiagent systems with lumped disturbance and application in multi flight simulators systems, The International Society of Automation Transactions, 74 (2018), 217-228.   Google Scholar

[35]

F. Zhang and W. Wang, Decentralized optimal control for the mean field LQG problem of multi-agent systems, International Journal of Innovative Computing Information and Control, 13 (2017), 55-66.   Google Scholar

[36]

D. ZhangZ. H. XuD. Srinivasan and L. Yu, Leader-follower consensus of multiagent systems with energy constraints: A markovian system approach, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47 (2017), 1727-1736.  doi: 10.1109/TSMC.2017.2677471.  Google Scholar

[37]

Z. Q. ZhangL. ZhangF. Hao and L. Wang, Leader-following consensus for linear and Lipschitz nonlinear multiagent systems with quantized communication, IEEE Transactions on Cybernetics, 47 (2017), 1970-1982.  doi: 10.1109/TCYB.2016.2580163.  Google Scholar

show all references

References:
[1]

H. B. DuY. G. He and Y. Y. Cheng, Finite-time synchronization of a class of second-order nonlinear multi-agent systems using output feedback control, IEEE Transactions on Circuits and Systems I: Regular Papers, 61 (2014), 1778-1788.  doi: 10.1109/TCSI.2013.2295012.  Google Scholar

[2]

H. B. DuG. H. WenG. R. ChenJ. D. Cao and F. E. Alsaadi, A distributed finite-time consensus algorithm for higher-order leaderless and leader-following multiagent systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47 (2017), 1625-1634.  doi: 10.1109/TSMC.2017.2651899.  Google Scholar

[3]

M.-M. DuanC.-L. Liu and F. Liu, Event-triggered consensus seeking of heterogeneous first-order agents with input delay, IEEE Access, 5 (2017), 5215-5223.  doi: 10.1109/ACCESS.2017.2696026.  Google Scholar

[4]

K. FathianT. H. Summers and N. R. Gans, Robust distributed formation control of agents with higher-order dynamics, IEEE Control Systems Letters, 2 (2018), 495-500.  doi: 10.1109/LCSYS.2018.2841941.  Google Scholar

[5]

L. Gao, J. Li, X. Zhu and W. Chen, Leader-following consensus of linear multi-agent systems with state-observer under switching topologies, 2012 12th International Conference on Control Automation Robotics and Vision, (2012), 572–577. Google Scholar

[6]

G. X. GuL. Marinovici and F. L. Lewis, Consensusability of discrete-time dynamic multiagent systems, IEEE Transactions on Automatic Control, 57 (2012), 2085-2089.  doi: 10.1109/TAC.2011.2179431.  Google Scholar

[7]

G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge University Press, 1952.  Google Scholar

[8]

B. HouF. C. SunH. B. Li and G. B. Liu, Consensus of second-order multi-agent systems with time-varying delays and antagonistic interactions, Tsinghua Science and Technology, 20 (2015), 205-211.  doi: 10.1109/TST.2015.7085634.  Google Scholar

[9]

H. H. JiH. T. ZhangZ. Y. YeH. ZhangB. W. Xu and G. R. Chen, Stochastic consensus control of second-order nonlinear multiagent systems with external disturbances, IEEE Transactions on Control of Network Systems, 5 (2018), 1585-1596.  doi: 10.1109/TCNS.2017.2736959.  Google Scholar

[10]

S. H. LiH. B. Du and X. Z. Lin, Finite-time consensus algorithm for multiagent systems with double-integrator dynamics, Automatica J. IFAC, 47 (2011), 1706-1712.  doi: 10.1016/j.automatica.2011.02.045.  Google Scholar

[11]

Z. K. LiZ. S. Duan and F. L. Lewis, Distributed robust consensus control of multi-agent systems with heterogeneous matching uncertainties, Automatica J. IFAC, 50 (2014), 883-889.  doi: 10.1016/j.automatica.2013.12.008.  Google Scholar

[12]

H. Q. LiX. F. LiaoT. W. HuangW. Zhu and Y. B. Liu, Second-order global consensus in multiagent networks with random directional link failure, IEEE Transactions on Neural Networks and Learning Systems, 26 (2015), 565-575.  doi: 10.1109/TNNLS.2014.2320274.  Google Scholar

[13]

G. P. LiX. Y. Wang and S. H. Li, Finite-time output consensus of higher-order multiagent systems with mismatched disturbances and unknown state elements, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49 (2019), 2751-2581.  doi: 10.1109/TSMC.2017.2759095.  Google Scholar

[14]

G. P. LiX. Y. Wang and S. H. Li, Distributed composite output consensus protocols of higher-order multi-agent systems subject to mismatched disturbances, IET Control Theory and Applications, 11 (2017), 1162-1172.  doi: 10.1049/iet-cta.2016.0814.  Google Scholar

[15]

X. D. LiX. Y. Yang and T. W. Huang, Persistence of delayed cooperative models: Impulsive control method, Applied Mathematics and Computation, 342 (2019), 130-146.  doi: 10.1016/j.amc.2018.09.003.  Google Scholar

[16]

C.-L. LiuL. ShanY.-Y. Chen and Y. Zhang, Average-consensus filter of first-order multi-agent systems with disturbances, IEEE Transactions on Circuits and Systems II: Express Briefs, 65 (2018), 1763-1767.  doi: 10.1109/TCSII.2017.2762723.  Google Scholar

[17]

C. Q. MaT. Li and J. F. Zhang, Consensus control for leader-following multi-agent systems with measurement noise, Journal of Systems Science and Complexity, 23 (2010), 35-49.  doi: 10.1007/s11424-010-9273-4.  Google Scholar

[18]

Z. Y. MengW. Ren and Z. You, Distributed finite-time attitude containment control for multiple rigid bodies, Autonmatica, 46 (2010), 2092-2099.  doi: 10.1016/j.automatica.2010.09.005.  Google Scholar

[19]

S. Mondal and R. Su, Disturbance observer based consensus control for higher order multi-agent systems with mismatched uncertainties, 2016 American Control Conference, (2016), 2826–2831. doi: 10.1109/ACC.2016.7525347.  Google Scholar

[20]

C. PengJ. Zhang and Q.-L. Han, Consensus of multiagent systems with nonlinear dynamics using an integrated sampled-data-based event-triggered communication scheme, IEEE Transactions on Systems, Man and Cybernetics: Systems, 49 (2019), 589-599.  doi: 10.1109/TSMC.2018.2814572.  Google Scholar

[21]

Z. R. QiuL. H. Xie and Y. G. Hong, Quantized leaderless and leader-following consensus of high-order multi-agent systems with limited data rate, IEEE Transactions on Automatic Control, 61 (2016), 2432-2447.  doi: 10.1109/TAC.2015.2495579.  Google Scholar

[22]

M. RehanA. Jameel and C. K. Ahn, Distributed consensus control of one-sided Lipschitz nonlinear multiagent systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48 (2018), 1297-1308.  doi: 10.1109/TSMC.2017.2667701.  Google Scholar

[23]

W. Ren and E. Atkins, Distributed multi-agent systems under dynamically changing interaction topologies, IEEE Transactions on Automatic Control, 50 (2005), 655-661.   Google Scholar

[24]

C. RenZ. Shi and T. Du, Distributed observer-based leader-following consensus control for second-order stochastic multi-agent systems, IEEE Access, 6 (2018), 20077-20084.  doi: 10.1109/ACCESS.2018.2820813.  Google Scholar

[25]

L. N. RongJ. W. LuS. Y. Xu and Y. M. Chu, Reference model-based containment control of multi-agent systems with higher-order dynamics, IET Control Theory and Applications, 8 (2014), 796-802.  doi: 10.1049/iet-cta.2013.0148.  Google Scholar

[26]

P. Shi and Q. Shen, Cooperative control of multi-agent systems with unknown state-dependent controlling effects, IEEE Transactions on Automation Science and Engineering, 12 (2015), 827-834.   Google Scholar

[27]

S. Z. Su and Z. L. Lin, Distributed synchronization control of multi-agent systems with switching directed communication topologies and unknown nonlinearities, 2015 54th IEEE Conference on Decision and Control, (2015), 5444–5449. doi: 10.1109/CDC.2015.7403072.  Google Scholar

[28]

X. H. WangY. G. Hong and H. B. Ji, Distributed optimization for a class of nonlinear multiagent systems with disturbance rejection, IEEE Transactions on Cybernetics, 46 (2016), 1655-1666.  doi: 10.1109/TCYB.2015.2453167.  Google Scholar

[29]

X. Y. WangS. H. LiX. H. Yu and J. Yang, Distributed active anti-disturbance consensus for leader-follower higher-order multi-agent systems with mismatched disturbances, IEEE Transactions on Automatic Control, 62 (2017), 5795-5801.  doi: 10.1109/TAC.2016.2638966.  Google Scholar

[30]

J. H. WangY. L. XuY. Xu and D. D. Yang, Time-varying formation for high-order multi-agent systems with external disturbances by event-triggered integral sliding mode control, Appl. Math. Comput., 359 (2019), 333-343.  doi: 10.1016/j.amc.2019.04.066.  Google Scholar

[31]

Z. WuY. XuY. PanP. Shi and Q. Wang, Event-triggered pinning control for consensus of multiagent systems with quantized information, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48 (2018), 1929-1938.   Google Scholar

[32]

D. YangX. D. Li and J. L. Qiu, Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback, Nonlinear Analysis: Hybrid Systems, 32 (2019), 294-305.  doi: 10.1016/j.nahs.2019.01.006.  Google Scholar

[33]

Z. Y. YuH. J. Jiang and C. Hu, Leader-following consensus of fractional-order multi-agent systems under fixed topology, Neurocomputing, 149 (2015), 613-620.  doi: 10.1016/j.neucom.2014.08.013.  Google Scholar

[34]

C. Zhang, Distributed ESO based cooperative tracking control for high-order nonlinear multiagent systems with lumped disturbance and application in multi flight simulators systems, The International Society of Automation Transactions, 74 (2018), 217-228.   Google Scholar

[35]

F. Zhang and W. Wang, Decentralized optimal control for the mean field LQG problem of multi-agent systems, International Journal of Innovative Computing Information and Control, 13 (2017), 55-66.   Google Scholar

[36]

D. ZhangZ. H. XuD. Srinivasan and L. Yu, Leader-follower consensus of multiagent systems with energy constraints: A markovian system approach, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47 (2017), 1727-1736.  doi: 10.1109/TSMC.2017.2677471.  Google Scholar

[37]

Z. Q. ZhangL. ZhangF. Hao and L. Wang, Leader-following consensus for linear and Lipschitz nonlinear multiagent systems with quantized communication, IEEE Transactions on Cybernetics, 47 (2017), 1970-1982.  doi: 10.1109/TCYB.2016.2580163.  Google Scholar

Figure 1.  The topology of the multi-agent system
Figure 2.  Position states of agents
Figure 3.  Velocity states of agents
Figure 4.  Acceleration states of agents
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