Globally repetitive learning consensus control of unknown nonlinear multi-agent systems with uncertain time-varying parameters. (English) Zbl 1478.93620
Summary: This paper studies the globally repetitive learning leader-following consensus for a class of unknown nonlinear multi-agent systems with uncertain periodic time-varying parameters. Neural networks are used as the feed-forward compensators to model some unknown nonlinear system functions. According to the different distributions of agents in the network topology, and by learning periodic uncertainties, a new hybrid repetitive learning control protocol is presented based on Lyapunov theory. Meanwhile, the proposed learning control protocol can guarantee that all the followers can track the leader asymptotically. Moreover, the boundedness of all the signals is ensured. Finally, three simulation examples are provided to verify the effectiveness of the proposed scheme.
MSC:
| 93D50 | Consensus |
| 93A16 | Multi-agent systems |
| 93A13 | Hierarchical systems |
| 93C10 | Nonlinear systems in control theory |
| 93B47 | Iterative learning control |
References:
| [1] | Lewis, F. L.; Zhang, H. W.; Hengster-Movric, K.; Das, A., Cooperative Control of Multi-Agent Systems: Optimal and Adaptive Design Approaches (2014), Springer-Verlag: Springer-Verlag London · Zbl 1417.93015 |
| [2] | Yang, S.; Xu, J. X.; Li, X.; Shen, D., Iterative Learning Control for Multi-Agent Systems Coordination (2017), Wiley |
| [3] | Uchiyama, M., Formation of high-speed motion pattern of a mechanical arm by trial, Trans. SICE, 14, 706-712 (1978) |
| [4] | Hara, S.; Yamamoto, Y.; Omata, T.; Nakano, M., Repetitive control system: a new type servo system for periodic exogenous signals, IEEE Trans. Autom. Control, 33, 659-668 (1988) · Zbl 0662.93027 |
| [5] | Chen, C.; Wen, C. Y.; Liu, Z. Y.; Xie, K.; Zhang, Y.; Chen, C. L.P., Adaptive consensus of nonlinear multi-agent systems with non-identical partially unknown control directions and bounded modelling errors, IEEE Trans. Autom. Control, 62, 9, 4654-4659 (2017) · Zbl 1390.93022 |
| [6] | Chen, J. X.; Li, J. M.; Yuan, X. X., Distributed fuzzy adaptive consensus for high-order multi-agent systems with an imprecise communication topology structure, Fuzzy Sets Syst. (2020) |
| [7] | Li, Z. K.; Ren, W.; Liu, X. D.; Fu, M. Y., Consensus of multi-agent systems with general linear and Lipschitz nonlinear dynamics using distributed adaptive protocols, IEEE Trans. Autom. Control, 58, 1786-1791 (2013) · Zbl 1369.93032 |
| [8] | Ding, Z., Adaptive consensus output regulation of a class of nonlinear systems with unknown high-frequency gain, Automatica, 51, 348-355 (2014) · Zbl 1309.93084 |
| [9] | Shahvali, M.; Shojaei, K., Distributed adaptive neural control of nonlinear multi-agent systems with unknown control directions, Nonlinear Dyn., 83, 2213-2228 (2016) · Zbl 1353.93063 |
| [10] | Hashim, H. A.; Sami, E. F.; Frank, L. L., Neuro-adaptive cooperative tracking control with prescribed performance of unknown higher-order nonlinear multi-agent systems, IEEE Trans. Fuzzy Syst., 92, 445-460 (2019) · Zbl 1414.93108 |
| [11] | Xu, J. X.; Tan, Y., Linear and Nonlinear Iterative Learning Control (2003), Springer · Zbl 1021.93002 |
| [12] | Jin, X., Adaptive iterative learning control for high-order nonlinear multi-agent systems consensus tracking, Syst. Control Lett., 89, 16-23 (2016) · Zbl 1335.93067 |
| [13] | Santosh, D., Iterative control for networked heterogeneous multi-agent systems with uncertainties, IEEE Trans. Autom. Control, 62, 431-437 (2016) · Zbl 1359.93173 |
| [14] | Li, J. S.; Liu, S. Y.; Li, J. M., Adaptive iterative learning protocol design for nonlinear multi-agent systems with unknown control direction, J. Frankl. Inst., 355, 4298-4314 (2018) · Zbl 1390.93445 |
| [15] | Shen, D.; Zhang, C.; Xu, J. X., Distributed learning consensus control based on neural networks for heterogeneous nonlinear multiagent systems, Int. J. Robust Nonlinear Control, 29, 4328-4347 (2019) · Zbl 1426.93306 |
| [16] | Li, J. S.; W. C. Ho, D.; Li, J. M., Distributed adaptive repetitive consensus control framework for uncertain nonlinear leader-follower multi-agent systems, J. Frankl. Inst., 352, 5342-5360 (2015) · Zbl 1395.93016 |
| [17] | Spong, M. W.; Hutchinson, S.; . Vidyasagar, M., Robot Modeling and Control (2006), Wiley: Wiley New York |
| [18] | Khalil, H., Nonliear Systems (1996), Prentice-Hall: Prentice-Hall New Jersey |
| [19] | Zhang, H. W.; Lewis, F. L., Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics, Automatica, 48, 1432-1439 (2012) · Zbl 1348.93144 |
| [20] | Yoshizawa, T., Stability Theory by Liapunov’s Second Method (1966), Mathematical Society of Japan: Mathematical Society of Japan Tokyo, Japan · Zbl 0144.10802 |
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