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Observer-Based Consensus of Higher-Order Nonlinear Heterogeneous Multiagent Systems with Unmatched Uncertainties: Application on Robotic Systems

Published online by Cambridge University Press:  14 November 2019

N. Rahimi ,
T. Binazadeh Open the ORCID record for T. Binazadeh [Opens in a new window]  and
M. Shasadeghi
N. Rahimi
Affiliation:
Department of Electrical and Electronic Engineering, Shiraz University of Technology, Shiraz, Iran, E-mails: [email protected]; [email protected]
T. Binazadeh*
Affiliation:
Department of Electrical and Electronic Engineering, Shiraz University of Technology, Shiraz, Iran, E-mails: [email protected]; [email protected]
M. Shasadeghi
Affiliation:
Department of Electrical and Electronic Engineering, Shiraz University of Technology, Shiraz, Iran, E-mails: [email protected]; [email protected]
*
*Corresponding author. E-mail: [email protected]
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Summary

The consensus of higher-order nonlinear heterogeneous multiagent systems with matched and unmatched uncertainties is studied in this paper. The distributed observer-based controllers for multiagent systems are achieved using a fixed-time sliding mode controller based on the disturbance observer. For this purpose, the disturbance observers are designed for finite-time estimation of matched and unmatched uncertainties. Using the estimated values, the fixed-time distributed sliding mode controllers are designed and the consensus protocol is achieved. In this regard, a theorem is proved, which guarantees the fixed-time convergence of consensus errors. The effectiveness of the proposed distributed controllers has been validated through simulations for two robotic multiagent systems and a numerical example.

Keywords

Fixed/finite-time stabilityConsensusNonlinear heterogeneous multiagent systemsDisturbances observerMatched and unmatched uncertaintiesRobotic multiagent systems
Type
Articles
Information
Robotica , Volume 38 , Issue 9 , September 2020 , pp. 1605 - 1626
Copyright
© Cambridge University Press 2019

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References

Chen, Y., Lu, J., Yu, X. and Hill, D. J., “Multi-agent systems with dynamical topologies: Consensus and applications,” IEEE. Circ. Syst. Mag. 13(3), 21–34 (2013).CrossRefGoogle Scholar
DeVries, L., Sims, A. and Kutzer, M. D., “Kernel design and distributed, self-triggered control for coordination of autonomous multi-agent configurations,” Robotica 36(7), 1077–1097 (2018).CrossRefGoogle Scholar
Li, S. and Wang, X., “Finite-time consensus and collision avoidance control algorithms for multiple AUVs,” Automatica 49(11), 3359–3367 (2013).CrossRefGoogle Scholar
Lou, X. and Cui, B., “Adaptive consensus filters for second-order distributed parameter systems using sensor networks,” Circ. Syst. Signal Process. 34(9), 2801–2818 (2015).CrossRefGoogle Scholar
Rahimi, N. and Binazadeh, T., “Distributed adaptive robust controller design for consensus in multi-agent system including robot arms with actuator saturation constraint,” Modares Mech. Eng. 19(7), 1759–1766 (2019).Google Scholar
Olfati-Saber, R., Fax, J. A. and Murray, R. M., “Consensus and cooperation in networked multi-agent systems,” Proc. IEEE 95(1), 215–233 (2007).CrossRefGoogle Scholar
He, X. and Wang, Q., “Distributed finite-time leaderless consensus control for double-integrator multi-agent systems with external disturbances,” Appl. Math. Comput. 295, 65–76 (2017).Google Scholar
Jenabzadeh, A., Safarinejadian, B. and Binazadeh, T., “Distributed tracking control of multiple nonholonomic mobile agents with input delay,” Trans. Inst. Meas. Control 41(3), 805–815 (2019).10.1177/0142331218771143CrossRefGoogle Scholar
Rahimi, N. and Binazadeh, T., “Distributed robust consensus control for nonlinear leader–follower multi-agent systems based on adaptive observer-based sliding mode,” J. Vib. Control 25(1), 109–121 (2019).CrossRefGoogle Scholar
Wang, W., Wen, C. and Huang, J., “Distributed adaptive asymptotically consensus tracking control of nonlinear multi-agent systems with unknown parameters and uncertain disturbances,” Automatica 77, 133–142 (2017).10.1016/j.automatica.2016.11.019CrossRefGoogle Scholar
Shi, S., Feng, H., Liu, W. and Zhuang, G., “Finite-time consensus of high-order heterogeneous multi-agent systems with mismatched disturbances and nonlinear dynamics,” Nonlinear Dyn. 96(2), 1317–1333 (2019).10.1007/s11071-019-04856-3CrossRefGoogle Scholar
Liu, X., Ho, D. W., Cao, J. and Xu, W., “Discontinuous observers design for finite-time consensus of multiagent systems with external disturbances,” IEEE Trans. Neur. Net. Learn. Syst. 28(11), 2826–2830 (2017).10.1109/TNNLS.2016.2599199CrossRefGoogle ScholarPubMed
Zhang, H., Yue, D., Yin, X., Hu, S. and Dou, C., “Finite-time distributed event-triggered consensus control for multi-agent systems,” Inf. Sci. 339, 132–142 (2016).CrossRefGoogle Scholar
Ning, B., Jin, J. and Zheng, J., “Fixed-time consensus for multi-agent systems with discontinuous inherent dynamics over switching topology,” Int. J. Syst. Sci. 48(10), 2023–2032 (2017).10.1080/00207721.2017.1308579CrossRefGoogle Scholar
Hong, H., Yu, W., Wen, G. and Yu, X., “Distributed robust fixed-time consensus for nonlinear and disturbed multi agent systems,” IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1464–1473 (2017).CrossRefGoogle Scholar
Ni, J., Tang, Y. and Shi, P., “A new fixed-time consensus tracking approach for second-order multiagent systems under directed communication topology,” IEEE Trans. Syst. Man Cybern. Syst. (2019).CrossRefGoogle Scholar
Ning, B., Han, Q. L. and Zuo, Z., “Practical fixed-time consensus for integrator-type multi-agent systems: A time base generator approach,” Automatica 105, 406–414, (2019).CrossRefGoogle Scholar
Chen, G., Song, Y. and Guan, Y., “Terminal sliding mode-based consensus tracking control for networked uncertain mechanical systems on digraphs,” IEEE Trans. Neur. Net. Learn. Syst. 29(3), 749–756 (2018).CrossRefGoogle ScholarPubMed
Niu, X., Liu, Y. and Man, Y., “Finite-time consensus tracking for multi-agent systems with inherent uncertainties and disturbances,” Int. J. Control , 92(6), 1415–1425 (2019).CrossRefGoogle Scholar
Wang, Q., Yu, Y. and Sun, C., “Distributed event-based consensus control of multi-agent system with matching nonlinear uncertainties,” Neurocomputing 272, 694–702 (2018).CrossRefGoogle Scholar
Hu, M., Guo, L., Hu, A. and Yang, Y., “Leader-following consensus of linear multi-agent systems with randomly occurring nonlinearities and uncertainties and stochastic disturbances,” Neurocomputing 149, 884–890 (2015).10.1016/j.neucom.2014.07.047CrossRefGoogle Scholar
Sun, F., Zhu, W., Li, Y. and Liu, F., “Finite-time consensus problem of multi-agent systems with disturbance,” J. Franklin Inst. 353(12), 2576–2587 (2016).CrossRefGoogle Scholar
Li, G., Wang, X. and Li, S., “Distributed composite output consensus protocols of higher-order multi-agent systems subject to mismatched disturbances,” IET Control Theory Appl. 11(8), 1162–1172 (2017).CrossRefGoogle Scholar
Wang, X., Li, S. and Lam, J., “Distributed active anti-disturbance output consensus algorithms for higher-order multi-agent systems with mismatched disturbances,” Automatica 74, 30–37 (2016).10.1016/j.automatica.2016.07.010CrossRefGoogle Scholar
Yu, S., Long, X. and Guo, G., “Continuous finite-time output consensus tracking of high-order agents with matched and unmatched disturbances,” IET Control Theory Appl. 10(14), 1716–1723 (2016).CrossRefGoogle Scholar
Wang, X., Li, S. and Chen, M. Z., “Composite backstepping consensus algorithms of leader-Follower higher-Order nonlinear multi agent systems subject to mismatched disturbances,” IEEE Trans. Cybern. 48(6), 1935–1946 (2018).CrossRefGoogle Scholar
Wang, X., Li, S., Yu, X. and Yang, J., “Distributed active anti-disturbance consensus for leader-follower higher-order multi-agent systems with mismatched disturbances,” IEEE Trans. Autom. Control 62(11), 5795–5801 (2017).CrossRefGoogle Scholar
Nguyen, D. H., “Distributed consensus design for a class of uncertain linear multi agent systems under unbalanced randomly switching directed topologies,” Math. Prob. Eng. 2018, 8081264 (2018).CrossRefGoogle Scholar
Fan, M. and Wang, M., “Second-order consensus for a class of uncertain multi-agent systems subject to input saturation,” Trans. Inst. Meas. Control 41(7),1957–1964 (2019).CrossRefGoogle Scholar
Lu, M. and Liu, L., “Robust Consensus of a Class of Heterogeneous Nonlinear Uncertain Multi-agent Systems Subject to Communication Constraints,” Chinese Control And Decision Conference (2018) pp. 74–81.Google Scholar
Ye, H., Li, M. and Luo, W., “Consensus protocols for heterogeneous multi agent systems with disturbances via integral sliding mode control,” Math. Prob. Eng. 2018, 1–6 (2018).Google Scholar
Feng, Y. and Zheng, W. X., “Adaptive tracking control for nonlinear heterogeneous multi-agent systems with unknown dynamics,” J. Franklin Inst. 356(5), 2780–2797 (2019).CrossRefGoogle Scholar
Meng, H., Chen, Z., Zhu, L. and Middleton, R., “Consensus of a class of second-order nonlinear heterogeneous multi-agent systems with uncertainty and communication delay,” Int. J. Robust Nonlinear Control 26(15), 3311–3329 (2016).CrossRefGoogle Scholar
Mondal, S., Su, R. and Xie, L., “Heterogeneous consensus of higher-order multi-agent systems with mismatched uncertainties using sliding mode control,” Int. J. Robust Nonlinear Control 27(13), 2303–2320 (2017).CrossRefGoogle Scholar
Bhat, S. P. and Bernstein, D. S., “Finite-time stability of continuous autonomous systems,” SIAM J. Control Optim. 38(3), 751–766 (2000).CrossRefGoogle Scholar
Polyakov, A., “Nonlinear feedback design for fixed-time stabilization of linear control systems,” IEE Trans. Autom. Control 57(8), 2106–2110 (2012).CrossRefGoogle Scholar
Tian, B., Zuo, Z. and Wang, H., “Leader–follower fixed-time consensus of multi-agent systems with high-order integrator dynamics,” Int. J. Control 90(7), 1420–1427 (2017).CrossRefGoogle Scholar
Shtessel, Y. B., Shkolnikov, I. A. and Levant, A., “Smooth second-order sliding modes: Missile guidance application,” Automatica 43(8), 1470–1476 (2007).CrossRefGoogle Scholar
Li, S. and Tian, Y. P., “Finite-time stability of cascaded time-varying systems,” Int. J. Control 80(4), 646–657 (2007).CrossRefGoogle Scholar
Zhang, H., Lewis, F. and Qu, Z., “Lyapunov, adaptive, and optimal design techniques for cooperative systems on directed communication graphs,” IEEE Trans. Ind. Electron. 59(7), 3026–3041 (2012).CrossRefGoogle Scholar
Li, J., Yang, Y., Hu, C. and Guan, X., “Fixed-time backstepping control design for high-order strict-feedback non-linear systems via terminal sliding mode,” IET Control Theory Appl. 11(8), 1184–1193 (2016).CrossRefGoogle Scholar