Abstract
This paper probes into the problem of predefined-time consensus tracking for a class of second-order multi-agent systems (MASs) subject to external disturbances based on a predefined-time observer. A predefined-time control strategy based on the use of terminal sliding mode control method is proposed, which can achieve consensus tracking in a predefined time. Firstly, the observer is designed so that observed states and leader states reach consensus. Secondly, according to the designed controller, states of each agent and observed states achieve consensus, namely, leader-following consensus is realized. By employing Lyapunov stability theory, some sufficient criteria are obtained to achieve predefined-time consensus tracking for second-order MASs with disturbances. Finally, some numerical examples are presented to prove the validity of our designs.
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References
R. Aldana-Lopez, D. Gómez-Gutiérrez, J.D. Esteban Jiménez-Rodríguez, M. Defoort. Sánchez-Torres, Enhancing the settling time estimation of a class of fixed-time stable systems. Int. J. Robust Nonlinear Control 29(12), 4135–4148 (2019)
R. Aldana-López, D. Gómez-Gutiérez, M. Defoort, J.D. Sánchez-Torres, A.J. Muñoz-Vázquez, A class of robust consensus algorithms with predefined-time convergence under switching topologies. Int. J. Robust Nonlinear Control 29(17), 6179–6198 (2019)
G. Basile, G. Marro, Controlled and Conditioned Invariants in Linear System Theory (Prentice Hall, Upper Saddle River, 1992)
S. Chen, B. Chen, F. Shi, Distributed fault-tolerant consensus protocol for fuzzy multi-agent systems. Circ. Syst. Signal Pr. 38(2), 611–624 (2019)
T. Chen, S. Peng, Z. Zhang, Finite-time and fixed-time consensus of nonlinear stochastic multi-agent systems with rous and rons via impulsive control. IEEE Access 7, 136630–136640 (2019)
Q. Deng, W. Jie, T. Han, Q. Yang, X. Cai, Fixed-time bipartite consensus of multi-agent systems with disturbances. Phys. A 516, 37–49 (2019)
J. Fu, G. Wen, W. Yu, Z. Ding, Finite-time consensus for second-order multi-agent systems with input saturation. IEEE Trans. Circuits Syst. II Exp. Briefs 65(11), 1758–1762 (2017)
J. Fu, J. Wang, Finite-time consensus for multi-agent systems with globally bounded convergence time under directed communication graphs. Int. J. Control 90(9), 1807–1817 (2017)
H. Gao, J. Lam, G. Chen, New criteria for synchronization stability of general complex dynamical networks with coupling delays. Phys. Lett. A 360(2), 263–273 (2006)
T. Han, Z. Guan, B. Xiao, H. Yan, Bipartite average tracking for multi-agent systems with disturbances: finite-time and fixed-time convergence. IEEE Trans. Circuits Syst. I Reg. Papers 68(10), 4393–4402 (2021)
Y. Huang, Y. Jia, Fixed-time consensus tracking control of second-order multi-agent systems with inherent nonlinear dynamics via output feedback. Nonlinear Dyn. 91, 1289–1306 (2018)
E. Jiménez-Rodríguez, A.J. Muñoz-Vázquez, J.D. Sánchez-Torres, M. Defoort, A.G. Loukianov, A Lyapunov-like characterization of predefined-time stability. IEEE Transactions on Automatic Control 65(11), 4922–4927 (2020)
E. Jiménez-Rodríguez, J.D. Sánchez-Torres, A.G. Loukianov, On optimal predefined-time stabilization. Int. J. Robust Nonlinear Control 27(17), 3620–3642 (2017)
F. Li, G. Wang, Y. Hou, C. Wang, Q. Li, Output feedback consensus of nonlinear multi-agent systems under directed topologies. Circuits Syst. Signal Process. 42(1), 216–233 (2023)
G. Li, Y. Wu, X. Liu, Adaptive fixed-time consensus tracking control method for second-order multi-agent systems with disturbances. J. Frankl. Inst. 357, 1516–1531 (2020)
K. Li, C. Hua, X. You, C.K. Ahn, Output feedback predefined-time bipartite consensus control for high-order nonlinear multiagent systems. IEEE Trans. Circuits Syst. I Reg. Papers 68(7), 3069–3078 (2021)
L. Li, P. Shi, Y. Zhao, D. Zhou, W. Xing, Containment control of multi-agent systems with uniform quantization. Circ. Syst. Signal Pr. 38(9), 3952–3970 (2019)
C. Liang, M. Ge, Z. Liu, G. Ling, F. Liu, Predefined-time formation tracking control of networked marine surface vehicles. Control Eng. Pract. 107, 104682 (2021)
Z. Lin, Y. Jia, J. Yu, Adaptive finite-time bipartite consensus for second-order multi-agent systems with antagonistic interactions. IEEE Control Syst. Lett. 102, 22–31 (2017)
X. Liu, J. Cao, C. Xie, Finite-time and fixed-time bipartite consensus of multi-agent systems under a unified discontinuous control protocol. J. Frankl. Inst. 356, 734–751 (2019)
Y. Liu, Y. Zhao, G. Chen, Finite-time formation tracking control for multiple vehicles: a motion planning approach. Int. J. Robust Nonlinear Control 26(14), 3130–3149 (2016)
D. Meng, Y. Jia, J. Du, Nonlinear finite-time bipartite consensus protocol for multi-agent systems associated with signed graphs. Int. J. Control 88(10), 2074–2085 (2015)
D. Meng, Z. Zuo, Signed-average consensus for networks of agents: a nonlinear fixed-time convergence protocol. Nonlinear Dyn. 85(1), 155–165 (2016)
B. Ning, X. Yu, G. Wen, Z. Cao, Finite-time bipartite tracking control for double-integrator networked systems with cooperative and antagonistic interactions. IEEE Trans. Circuits Syst. I Reg. Papers 67(12), 5223–5232 (2020)
A. Polyakov, Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans. Autom. Control 57(8), 2106–2110 (2011)
J. Qin, H. Gao, W. Zheng, Consensus strategy for a class of multi-agents with discrete second-order dynamics. Int. J. Robust Nonlinear Control 22(4), 437–452 (2012)
J.D. Sanchez-Torres, D. Gomez-Gutierrez, E. Lopez, A.G. Loukianov, A class of predefined-time stable dynamical systems. IMA J. Math. Control Inf. 35, i1–i29 (2018)
Z. Shi, S. Hong, J. Chen, K. Chen, Y. Sun, Particle filter-based synchronization of chaotic Colpitts circuits combating AWGN channel distortion. Circ. Syst. Signal Pr. 27(6), 833–845 (2008)
F. Sun, P. Liu, H. Li, W. Zhu, Fixed-time consensus of heterogeneous multi-agent systems based on distributed observer. Int. J. Syst. Sci. 52(9), 1780–1789 (2021)
H. Wang, W. Yu, G. Wen, G. Chen, Finite-time bipartite consensus for multi-agent systems on directed signed networks. IEEE Trans. Circuits Syst. I Reg. Papers 65(12), 4336–4348 (2018)
G. Wen, H. Wang, X. Yu, W. Yu, Bipartite tracking consensus of linear multi-agent systems with a dynamic leader. IEEE Trans. Circuits Syst. II Exp. Briefs 65(9), 1204–1208 (2017)
Y. Wu, R. Lu, H. Li, S. He, Synchronization control for network systems with communication constraints. IEEE Trans. Neural Netw. Learn. Syst. 30(10), 3150–3160 (2019)
S. Xie, Q. Chen, Adaptive nonsingular predefined-time control for attitude stabilization of rigid spacecrafts. IEEE Trans. Circuits Syst. II Exp. Briefs 69(1), 189–193 (2021)
D. Yao, H. Li, R. Lu, Y. Shi, Event-triggered guaranteed cost leader-following consensus control of second-order nonlinear multiagent systems. IEEE Trans. Syst. Man Cybern. 52(4), 2615–2624 (2021)
S. Yu, X. Yu, B. Shirinzadeh, Z. Man, Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica 41(11), 1957–1964 (2005)
W. Yu, Y. Li, G. Wen, X. Yu, J. Cao, Observer design for tracking consensus in second-order multi-agent systems: fractional order less than two. IEEE Trans. Autom. Control 62(2), 894–900 (2016)
B. Zhang, Y. Jia, Fixed-time consensus protocols for multi-agent systems with linear and nonlinear state measurements. Nonlinear Dyn. 82(4), 1683–1690 (2015)
W. Zou, P. Shi, Z. Xiang, Y. Shi, Finite-time consensus of second-order switched nonlinear multi-agent systems. IEEE Trans. Neural Netw. Learn. Syst. 31(5), 1757–1762 (2019)
W. Zuo, K. Qian, Z. Xiang, Fixed-time consensus for a class of heterogeneous nonlinear multiagent systems. IEEE Trans. Circuits Syst. II Express Briefs 67(7), 1279–1283 (2019)
Z. Zuo, Nonsingular fixed-time consensus tracking for second-order multi-agent networks. Automatica 54, 305–309 (2015)
Funding
This work was funded by the National Natural Science Foundation of China (62071173 and 61971181) and the Natural Science Foundation of Hubei Province (2022CFB479).
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Lu, L., Han, T., Xiao, B. et al. Distributed Observer-Based Predefined-Time Consensus Control for Second-Order Multi-agent Systems. Circuits Syst Signal Process 42, 7099–7116 (2023). https://doi.org/10.1007/s00034-023-02449-5
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DOI: https://doi.org/10.1007/s00034-023-02449-5