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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 |
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.
Keywords:
Fully distributed consensus,
higher-order nonlinear systems,
multi-agent systems,
unmatched disturbances,
back-stepping.
Mathematics Subject Classification:
Primary: 58F15, 58F17; Secondary: 53C35.
Citation:
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
![]()
References:
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H. B. Du, Y. 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. |
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H. B. Du, G. H. Wen, G. R. Chen, J. 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. |
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M.-M. Duan, C.-L. Liu and F. Liu,
Event-triggered consensus seeking of heterogeneous first-order agents with input delay, IEEE Access, 5 (2017), 5215-5223.
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K. Fathian, T. H. Summers and N. R. Gans,
Robust distributed formation control of agents with higher-order dynamics, IEEE Control Systems Letters, 2 (2018), 495-500.
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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. |
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G. X. Gu, L. Marinovici and F. L. Lewis,
Consensusability of discrete-time dynamic multiagent systems, IEEE Transactions on Automatic Control, 57 (2012), 2085-2089.
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G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge University Press, 1952. |
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B. Hou, F. C. Sun, H. 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.
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H. H. Ji, H. T. Zhang, Z. Y. Ye, H. Zhang, B. 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.
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S. H. Li, H. B. Du and X. Z. Lin,
Finite-time consensus algorithm for multiagent systems with double-integrator dynamics, Automatica J. IFAC, 47 (2011), 1706-1712.
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H. Q. Li, X. F. Liao, T. W. Huang, W. 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. |
| [13] |
G. P. Li, X. 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. |
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Persistence of delayed cooperative models: Impulsive control method, Applied Mathematics and Computation, 342 (2019), 130-146.
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C.-L. Liu, L. Shan, Y.-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.
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C. Q. Ma, T. 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. |
| [18] |
Z. Y. Meng, W. 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. |
| [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. |
| [20] |
C. Peng, J. 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. |
| [21] |
Z. R. Qiu, L. 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. |
| [22] |
M. Rehan, A. 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. |
| [23] |
W. Ren and E. Atkins,
Distributed multi-agent systems under dynamically changing interaction topologies, IEEE Transactions on Automatic Control, 50 (2005), 655-661.
|
| [24] |
C. Ren, Z. 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. |
| [25] |
L. N. Rong, J. W. Lu, S. 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. |
| [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.
|
| [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. |
| [28] |
X. H. Wang, Y. 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. |
| [29] |
X. Y. Wang, S. H. Li, X. 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. |
| [30] |
J. H. Wang, Y. L. Xu, Y. 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. |
| [31] |
Z. Wu, Y. Xu, Y. Pan, P. 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.
|
| [32] |
D. Yang, X. 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. |
| [33] |
Z. Y. Yu, H. 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. |
| [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.
|
| [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.
|
| [36] |
D. Zhang, Z. H. Xu, D. 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. |
| [37] |
Z. Q. Zhang, L. Zhang, F. 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. |
show all references
References:
| [1] |
H. B. Du, Y. 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. |
| [2] |
H. B. Du, G. H. Wen, G. R. Chen, J. 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. |
| [3] |
M.-M. Duan, C.-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. |
| [4] |
K. Fathian, T. 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. |
| [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. |
| [6] |
G. X. Gu, L. 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. |
| [7] |
G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge University Press, 1952. |
| [8] |
B. Hou, F. C. Sun, H. 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. |
| [9] |
H. H. Ji, H. T. Zhang, Z. Y. Ye, H. Zhang, B. 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. |
| [10] |
S. H. Li, H. 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. |
| [11] |
Z. K. Li, Z. 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. |
| [12] |
H. Q. Li, X. F. Liao, T. W. Huang, W. 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. |
| [13] |
G. P. Li, X. 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. |
| [14] |
G. P. Li, X. 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. |
| [15] |
X. D. Li, X. 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. |
| [16] |
C.-L. Liu, L. Shan, Y.-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. |
| [17] |
C. Q. Ma, T. 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. |
| [18] |
Z. Y. Meng, W. 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. |
| [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. |
| [20] |
C. Peng, J. 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. |
| [21] |
Z. R. Qiu, L. 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. |
| [22] |
M. Rehan, A. 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. |
| [23] |
W. Ren and E. Atkins,
Distributed multi-agent systems under dynamically changing interaction topologies, IEEE Transactions on Automatic Control, 50 (2005), 655-661.
|
| [24] |
C. Ren, Z. 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. |
| [25] |
L. N. Rong, J. W. Lu, S. 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. |
| [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.
|
| [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. |
| [28] |
X. H. Wang, Y. 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. |
| [29] |
X. Y. Wang, S. H. Li, X. 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. |
| [30] |
J. H. Wang, Y. L. Xu, Y. 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. |
| [31] |
Z. Wu, Y. Xu, Y. Pan, P. 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.
|
| [32] |
D. Yang, X. 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. |
| [33] |
Z. Y. Yu, H. 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. |
| [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.
|
| [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.
|
| [36] |
D. Zhang, Z. H. Xu, D. 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. |
| [37] |
Z. Q. Zhang, L. Zhang, F. 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. |
Figure 2.
Position states of agents
Figure 3.
Velocity states of agents
Figure 4.
Acceleration states of agents
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