Modeling of a non-linear multi-agent distributed control system
DOI:
https://doi.org/10.15282/jmes.16.4.2022.06.0730Keywords:
Non-linear multi-agent system, Lyapunov, Optimization, Leader-following consensusAbstract
The goal of our research aims to develop a mathematical model for consensus control system based on Lyapunov Theory and nonlinear dynamics functional equations. This paper describes a new solution that deals with the general-consensus problem and the leader-following consensus problem of non-linear multi-agent system (NMAS) in which the parameters of all follower agents can be different, and with an unforced agent as the leader in the multi-agent system (MAS). Different control rules were constructed for each different follower agent based on its own state variables and its communication with adjacent agents. Finally, numerical simulations are provided to demonstrate the feasibility of the developed mathematical model. The results have demonstrated the designed distributed control system satisfy the Lyapunov Theory since all the agents have converged to its steady state after a period of time.
References
K. Chen, J. Wang, and Y. Zhang, “Distributed consensus of nonlinear multi-agent systems on state-controlled switching topologies,” Entropy, vol. 18, no. 1, pp. 29, 2016.
J. T. Feddema, C. Lewis, and D. A. Schoenwald, “Decentralized control of cooperative robotic vehicles: theory and application,” IEEE Transactions on robotics and automation, vol. 18, no. 5, pp. 852-864, 2002.
D. Trentesaux, “Distributed control of production systems,” Engineering Applications of Artificial Intelligence, vol. 22, no. 7, pp. 971-978, 2009.
Y. Li, and C. Tan, “A survey of the consensus for multi-agent systems,” Systems Science & Control Engineering, vol. 7, no. 1, pp. 468-482, 2019.
S. He, Y. Xu, Y. Wu, Y. Li, and W. Zhong, “Adaptive consensus tracking of multi-robotic systems via using integral sliding mode control,” Neurocomputing, vol. 455, pp. 154-162, 2021.
M. Naserian, A. Ramazani, A. Khaki-Sedigh, and A. Moarefianpour, “Leader–follower consensus control for a nonlinear multi-agent robot system with input saturation and external disturbance,” Systems Science & Control Engineering, vol. 9, no. 1, pp. 260-271, 2021.
R. Resmi, S. Mija, and J. Jacob, "Consensus control of two wheeled mobile robots with time delay," 2020 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), pp. 1-6, 2020.
Y. Tang, X. Xing, H. R. Karimi, L. Kocarev, and J. Kurths, “Tracking control of networked multi-agent systems under new characterizations of impulses and its applications in robotic systems,” IEEE Transactions on Industrial Electronics, vol. 63, no. 2, pp. 1299-1307, 2015.
S. Zhang, and Y. Cao, “Consensus in networked multi-robot systems via local state feedback robust control,” International Journal of Advanced Robotic Systems, vol. 16, no. 6, pp. 1729881419893549, 2019.
L. He, J. Zhang, Y. Hou, X. Liang, and P. Bai, “Time-varying formation control for second-order discrete-time multi-agent systems with directed topology and communication delay,” IEEE Access, vol. 7, pp. 33517-33527, 2019.
L. He, J. Zhang, Y. Hou, X. Liang, and P. Bai, “Time-varying formation control for second-order discrete-time multi-agent systems with switching topologies and nonuniform communication delays,” IEEE Access, vol. 7, pp. 65379-65389, 2019.
X. Qu, Y. Wan, P. Zhou, and L. Li, “Consensus-Based Formation of Second-Order Multi-Agent Systems via Linear-Transformation-Based Partial Stability Approach,” IEEE Access, vol. 7, pp. 165420-165427, 2019.
L. Wang, X. Li, B. Liu, and Z. Zhang, “Consensus formation control and obstacle avoidance of multiagent systems with directed topology,” Mathematical Problems in Engineering, vol. 2020, 2020.
B. Kada, M. Khalid, and M. S. Shaikh, “Distributed cooperative control of autonomous multi-agent UAV systems using smooth control,” Journal of Systems Engineering and Electronics, vol. 31, no. 6, pp. 1297-1307, 2020.
H. Li, and X. Li, “Distributed consensus of heterogeneous linear time-varying systems on UAVs–USVs coordination,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 67, no. 7, pp. 1264-1268, 2019.
T. Z. Muslimov, and R. A. Munasypov, “Consensus-based cooperative control of parallel fixed-wing UAV formations via adaptive backstepping,” Aerospace science and technology, vol. 109, pp. 106416, 2021.
J. A. V. Trejo, M. A. Medina, J. A. V. Trejo, C. D. G. Beltrán, and J. G. Morales, “Robust observer-based leader-following consensus for multi-agent systems,” IEEE Latin America Transactions, vol. 19, no. 11, pp. 1949-1958, 2021.
Y. Wang, Z. Cheng, and M. Xiao, “UAVs’ formation keeping control based on Multi–Agent system consensus,” IEEE Access, vol. 8, pp. 49000-49012, 2020.
B. Liu, H.-T. Zhang, Y. Wu, and B. Hu, "Distributed consensus control of multi-USV systems," International Conference on Intelligent Robotics and Applications, pp. 628-635, 2017.
L. Wang, W. Yue, and R. Zhang, “Consensus for multiple unmanned surface vehicle (MUSV) systems with Markov switching topologies,” Polish Maritime Research, 2019.
X. Yang, W. Wang, and P. Huang, “Distributed optimal consensus with obstacle avoidance algorithm of mixed-order UAVs–USVs–UUVs systems,” ISA transactions, vol. 107, pp. 270-286, 2020.
Z. Yan, Y. Wu, Y. Liu, H. Ren, and X. Du, “Leader-following multiple unmanned underwater vehicles consensus control under the fixed and switching topologies with unmeasurable disturbances,” Complexity, vol. 2020, pp. 1-26, 2020.
F. Derakhshan, and S. Yousefi, “A review on the applications of multiagent systems in wireless sensor networks,” International Journal of Distributed Sensor Networks, vol. 15, no. 5, 2019.
M. Zheng, C.-L. Liu, and F. Liu, “Average-consensus tracking of sensor network via distributed coordination control of heterogeneous multi-agent systems,” IEEE Control Systems Letters, vol. 3, no. 1, pp. 132-137, 2018.
F. Wang, and Y. Yang, “On leaderless and leader-following consensus for heterogeneous nonlinear multiagent systems via discontinuous distributed control protocol,” Mathematical Problems in Engineering, vol. 2018, 2018.
Z. Zhang, S. Chen, and Y. Zheng, “Leader-following scaled consensus of second-order multi-agent systems under directed topologies,” International Journal of Systems Science, vol. 50, no. 14, pp. 2604-2615, 2019.
H. Su, M. Z. Chen, J. Lam, and Z. Lin, “Semi-global leader-following consensus of linear multi-agent systems with input saturation via low gain feedback,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 60, no. 7, pp. 1881-1889, 2013.
H. Su, Y. Qiu, and L. Wang, “Semi-global output consensus of discrete-time multi-agent systems with input saturation and external disturbances,” ISA transactions, vol. 67, pp. 131-139, 2017.
L. Shi, Y. Li, and Z. Lin, "Semi-global leader-following output consensus of discrete-time linear multi-agent systems with input saturation," 2018 IEEE International Conference on Real-time Computing and Robotics (RCAR). pp. 354-359, 2018.
L. Shi, Z. Zhao, and Z. Lin, “Robust semi-global leader-following practical consensus of a group of linear systems with imperfect actuators,” Science China Information Sciences, vol. 60, no. 7, pp. 1-12, 2017.
Z. Meng, Z. Zhao, and Z. Lin, “On global leader-following consensus of identical linear dynamic systems subject to actuator saturation,” Systems & Control Letters, vol. 62, no. 2, pp. 132-142, 2013.
Z. Zhao, and Z. Lin, “Global leader-following consensus of a group of general linear systems using bounded controls,” Automatica, vol. 68, pp. 294-304, 2016.
Y. Xie, and Z. Lin, “Global consensus of multi-agent systems with intermittent directed communication in the presence of actuator saturation,” International Journal of Robust and Nonlinear Control, vol. 30, no. 18, pp. 8469-8484, 2020.
Y. Xin, Y. Li, X. Huang, and Z. Cheng, “Consensus of third-order nonlinear multi-agent systems,” Neurocomputing, vol. 159, pp. 84-89, 2015.
W. Zhu, and D. Cheng, “Leader-following consensus of second-order agents with multiple time-varying delays,” Automatica, vol. 46, no. 12, pp. 1994-1999, 2010.
G. Wen, Z. Peng, A. Rahmani, and Y. Yu, “Distributed leader-following consensus for second-order multi-agent systems with nonlinear inherent dynamics,” International Journal of Systems Science, vol. 45, no. 9, pp. 1892-1901, 2014.
N. Huang, Z. Duan, and Y. Zhao, “Leader-following consensus of second-order non-linear multi-agent systems with directed intermittent communication,” IET Control Theory & Applications, vol. 8, no. 10, pp. 782-795, 2014.
B. Tian, Z. Zuo, and H. Wang, “Leader–follower fixed-time consensus of multi-agent systems with high-order integrator dynamics,” International Journal of Control, vol. 90, no. 7, pp. 1420-1427, 2017.
Y. Zhao, Z. Li, and Z. Duan, “Distributed consensus tracking of multi-agent systems with nonlinear dynamics under a reference leader,” International Journal of Control, vol. 86, no. 10, pp. 1859-1869, 2013.
B. Cui, C. Zhao, T. Ma, and C. Feng, “Leader-following consensus of nonlinear multi-agent systems with switching topologies and unreliable communications,” Neural Computing and Applications, vol. 27, no. 4, pp. 909-915, 2016.
Y. Shi, Y. Yin, S. Wang, Y. Liu, and F. Liu, “Distributed leader-following consensus of nonlinear multi-agent systems with nonlinear input dynamics,” Neurocomputing, vol. 286, pp. 193-197, 2018.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Universiti Malaysia Pahang Publishing
This work is licensed under a Creative Commons Attribution 4.0 International License.
