Consensus tracking of fractional-order multiagent systems via fractional-order iterative learning control. (English) Zbl 1432.93021
Summary: In this work, the consensus problem of fractional-order multiagent systems with the general linear model of fixed topology is studied. Both distributed \(P D^\alpha \)-type and \(D^\alpha \)-type fractional-order iterative learning control (FOILC) algorithms are proposed. Here, a virtual leader is introduced to generate the desired trajectory, fixed communication topology is considered, and only a subset of followers can access the desired trajectory. The convergence conditions are proved using graph theory, fractional calculus, and \(\lambda\) norm theory. The theoretical analysis shows that the output of each agent completely tracks the expected trajectory in a limited time as the iteration number increases for both \(P D^\alpha \)-type and \(D^\alpha \)-type FOILC algorithms. Extensive numerical simulations are given to demonstrate the feasibility and effectiveness.
MSC:
| 93A16 | Multi-agent systems |
| 93C85 | Automated systems (robots, etc.) in control theory |
| 93D50 | Consensus |
References:
| [1] | Vanek, B.; Peni, T.; Bokor, J.; Balas, G., Practical approach to real-time trajectory tracking of UAV formations, Proceedings of the American Control Conference |
| [2] | Meng, D.; Jia, Y., Finite-time consensus for multi-agent systems via terminal feedback iterative learning, IET Control Theory & Applications, 5, 18, 2098-2110 (2011) · doi:10.1049/iet-cta.2011.0047 |
| [3] | Ge, X.; Han, Q.-L., Distributed formation control of networked multi-agent systems using a dynamic event-triggered communication mechanism, IEEE Transactions on Industrial Electronics, 64, 10, 8118-8127 (2017) · doi:10.1109/tie.2017.2701778 |
| [4] | Liu, J.; Chen, W.; Qin, K. Y.; Li, P., Consensus of multi-integral fractional-order multi-agent systems with nonuniform time-delays, Complexity, 2018 (2018) · Zbl 1407.93025 · doi:10.1155/2018/8154230 |
| [5] | Olfati-Saber, R.; Murray, R. M., Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49, 9, 1520-1533 (2004) · Zbl 1365.93301 · doi:10.1109/tac.2004.834113 |
| [6] | Li, Z.; Duan, Z.; Chen, G., Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint, EEE Transactions on Circuits and Systems I, 57, 1, 213-224 (2010) · Zbl 1468.93137 · doi:10.1109/tcsi.2009.2023937 |
| [7] | Yu, W.; Chen, G.; Cao, M., Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems, Automatica, 46, 6, 1089-1095 (2010) · Zbl 1192.93019 · doi:10.1016/j.automatica.2010.03.006 |
| [8] | Wen, G.; Duan, Z.; Yu, W.; Chen, G., Consensus of multi-agent systems with nonlinear dynamics and sampled-data information: a delayed-input approach, International Journal of Robust and Nonlinear Control, 23, 6, 602-619 (2013) · Zbl 1273.93012 · doi:10.1002/rnc.2779 |
| [9] | Fu, Q.; Li, X.-D.; Du, L.-L.; Xu, G.-Z.; Wu, J.-R., Consensus control for multi-agent systems with quasi-one-sided Lipschitz nonlinear dynamics via iterative learning algorithm, Nonlinear Dynamics, 91, 4, 2621-2630 (2018) · Zbl 1392.34022 · doi:10.1007/s11071-017-4035-7 |
| [10] | Deng, X.; Sun, X.; Liu, R.; Liu, S., Consensus control of time-varying delayed multiagent systems with high-order iterative learning control, International Journal of Aerospace Engineering, 2018 (2018) · doi:10.1155/2018/4865745 |
| [11] | Du, H.; Wen, G.; Yu, X.; Li, S.; Chen, M. Z. Q., Finite-time consensus of multiple nonholonomic chained-form systems based on recursive distributed observer, Automatica, 62, 236-242 (2015) · Zbl 1330.93008 · doi:10.1016/j.automatica.2015.09.026 |
| [12] | Du, H.; Jiang, C. R.; Wen, G. H.; Zhu, W.; Cheng, Y., Current sharing control for parallel DC-DC buck converters based on finite-time control technique, IEEE Transactions on Industrial Informatics, 15, 4, 2186-2198 (2018) · doi:10.1109/tii.2018.2864783 |
| [13] | Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J., Theory and Applications of Fractional Differential Equations (2006), Amsterdam, Netherlands: Elsevier, Amsterdam, Netherlands · Zbl 1092.45003 |
| [14] | Sabatier, J.; Agrawal, O. P.; Tenreiro Machado, J. A., Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering (2007), Berlin, Germany: Springer, Berlin, Germany · Zbl 1116.00014 |
| [15] | Liu, H.; Xie, G.; Yu, M., Necessary and sufficient conditions for containment control of fractional-order multi-agent systems, Neurocomputing, 323, 86-95 (2019) · doi:10.1016/j.neucom.2018.09.067 |
| [16] | Liu, X.; Zhang, Z.; Liu, H., Consensus control of fractional-order systems based on delayed state fractional order derivative, Asian Journal of Control, 19, 6, 2199-2210 (2017) · Zbl 1386.93014 · doi:10.1002/asjc.1493 |
| [17] | Liu, J.; Chen, W.; Qin, K.; Li, P.; Shi, M., Consensus of fractional-order multiagent systems with double integral and time delay, Mathematical Problems in Engineering, 2018 (2018) · Zbl 1426.93011 · doi:10.1155/2018/2850757 |
| [18] | Shen, J.; Cao, J.; Lu, J. Q., Consensus of fractional-order systems with non-uniform input and communication delays, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 226, 2, 271-283 (2012) · doi:10.1177/0959651811412132 |
| [19] | Liu, H.; Xie, G.; Gao, Y., Consensus of fractional-order double-integrator multi-agent systems, Neurocomputing, 340, 110-124 (2019) · doi:10.1016/j.neucom.2019.02.046 |
| [20] | Du, H.; Li, S.; Shi, P., Robust consensus algorithm for second-order multi-agent systems with external disturbances, International Journal of Control, 85, 12, 1913-1928 (2012) · Zbl 1401.93080 · doi:10.1080/00207179.2012.713515 |
| [21] | Zhu, W.; Wang, M.; Yang, C., Leader-following consensus of fractional-order multi-agent systems with general linear models, Proceedings of the 11th World Congress on Intelligent Control and Automation · doi:10.1109/wcica.2014.7053296 |
| [22] | Zhang, Y.; Wen, G.; Peng, Z.; Yu, Y.; Rahmani, A., Group multiple lags consensus of fractional-order nonlinear leader-following multi-agent systems via adaptive control, Transactions of the Institute of Measurement and Control, 41, 5, 1313-1322 (2019) · doi:10.1177/0142331218777570 |
| [23] | Yu, Y.; Ren, W.; Meng, Z., Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking, Systems & Control Letters, 59, 9, 522-529 (2010) · Zbl 1207.93103 · doi:10.1016/j.sysconle.2010.06.002 |
| [24] | Wang, L.; Xiao, F., Finite-time consensus problems for networks of dynamic agents, IEEE Transactions on Automatic Control, 55, 4, 950-955 (2010) · Zbl 1368.93391 · doi:10.1109/tac.2010.2041610 |
| [25] | Wang, X.; Hong, Y., Distributed finite-time \(χ\)-consensus algorithms for multi-agent systems with variable coupling topology, Journal of Systems Science and Complexity, 23, 2, 209-218 (2010) · Zbl 1197.93097 · doi:10.1007/s11424-010-7254-2 |
| [26] | Arimoto, S.; Kawamura, S.; Miyazaki, F., Bettering operation of robots by learning, Journal of Robotic Systems, 1, 2, 123-140 (1984) · doi:10.1002/rob.4620010203 |
| [27] | Sun, M. X.; Sam Ge, S. Z.; Mareels, M. Y., Adaptive repetitive learning control of robotic manipulators without the requirement for initial repositioning, IEEE Transactions on Robotics, 22, 3, 563-568 (2006) · doi:10.1109/tro.2006.870650 |
| [28] | Park, K. H., An average operator-based pd-type iterative learning control for variable initial state error, IEEE Transactions on Automatic Control, 50, 6, 865-869 (2005) · Zbl 1365.93557 · doi:10.1109/tac.2005.849249 |
| [29] | Meng, D.; Jia, Y., Iterative learning approaches to design finite-time consensus protocols for multi-agent systems, Systems & Control Letters, 61, 1, 187-194 (2012) · Zbl 1250.93012 · doi:10.1016/j.sysconle.2011.10.013 |
| [30] | Meng, D.; Jia, Y.; Du, J., Consensus seeking via iterative learning for multi-agent systems with switching topologies and communication time-delays, International Journal of Robust and Nonlinear Control, 26, 17, 3772-3790 (2016) · Zbl 1351.93009 · doi:10.1002/rnc.3534 |
| [31] | Wang, J.; Yang, T.; Staskevich, G.; Abbe, B., Approximately adaptive neural cooperative control for nonlinear multiagent systems with performance guarantee, International Journal of Systems Science, 48, 5, 909-920 (2017) · Zbl 1362.93078 · doi:10.1080/00207721.2016.1186242 |
| [32] | Bu, X. H.; Hou, Z. S.; Yu, F. S., Iterative learning control for a class of linear continuous-time switched systems, Control Theory and Applications, 29, 8, 1051-1056 (2012) · Zbl 1274.93137 |
| [33] | Podlubny, I., Fractional Differential Equations (1999), San Diego, CA, USA: Academic Press, San Diego, CA, USA · Zbl 0918.34010 |
| [34] | Diethelm, K.; Ford, N. J., Analysis of fractional differential equations, Journal of Mathematical Analysis and Applications, 265, 2, 229-248 (2002) · Zbl 1014.34003 · doi:10.1006/jmaa.2000.7194 |
| [35] | Godsil, C.; Royle, G., Algebraic Graph Theory (2001), New York, NY, USA: Springer-Verlag, New York, NY, USA · Zbl 0968.05002 |
| [36] | Sun, M.; Wang, D., Iterative learning control with initial rectifying action, Automatica, 38, 7, 1177-1182 (2002) · Zbl 1002.93508 · doi:10.1016/s0005-1098(02)00003-1 |
| [37] | Hong, Y.; Hu, J.; Gao, L., Tracking control for multi-agent consensus with an active leader and variable topology, Automatica, 42, 7, 1177-1182 (2006) · Zbl 1117.93300 · doi:10.1016/j.automatica.2006.02.013 |
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