Volume 15, Issue 3 (Journal of Control, V.15, N.3 Fall 2021)
JoC 2021, 15(3): 55-67 |
Back to browse issues page
Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
Ferdowsi H, Hashemi M. Adaptive neural control of nonlinear fractional order multi- agent systems in the presence of error constraintion. JoC 2021; 15 (3) :55-67
URL: http://joc.kntu.ac.ir/article-1-757-en.html
URL: http://joc.kntu.ac.ir/article-1-757-en.html
1- Islamic Azad University Najafabad Branch
Abstract: (5791 Views)
In this paper, the problem of fractional order multi-agent tracking control problem is considered. Uncertainties, error constraints, transient response suitability and desirable response tracking problems are the challenges in this study. Because of these problems and challenges, the adaptive control and Neural Networks approximators approaches are used in this study. In the first part of this article, the fractional order multi-agent systems are investigated with unknown parameters in the presence of error constraints. Then, a controller is designed on the basis of adaptive control and dynamic surface control so that the control objective of pursuing the desired output is achieved in the presence of the required constraints. The effective performance of the proposed controller is demonstrated by simulation by MATLAB software.
Keywords: Fractional- order dynamics, Multi-agent nonlinear systems, Unknown parameter, Neural Networks, Adaptive control
Type of Article: Research paper |
Subject:
Special
Received: 2020/04/16 | Accepted: 2021/01/14 | ePublished ahead of print: 2021/02/28 | Published: 2021/12/1
Received: 2020/04/16 | Accepted: 2021/01/14 | ePublished ahead of print: 2021/02/28 | Published: 2021/12/1
References
1. [1] R. Olfati-Saber and R. M. Murray, "Consensus problems in networks of agents with switching topology and time-delays", IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520-1533, Sep. 2004. [DOI:10.1109/TAC.2004.834113]
2. [2] W. Yu, W. Ren, W. X. Zheng, G. Chen, and J. Lü, "Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics", Automatica, vol. 49, no. 7, pp. 2107-2115, 2013. [DOI:10.1016/j.automatica.2013.03.005]
3. [3] Z. Meng, Z. Lin, and W. Ren, "Robust cooperative tracking for multiple non-identical second-order nonlinear systems, " Automatica, vol. 49, no. 8, pp. 2363-2372, 2013. [DOI:10.1016/j.automatica.2013.04.040]
4. [4] F. Chen, Y. Cao, and W. Ren, "Distributed average tracking of multiple time-varying reference signals with bounded derivatives", IEEE Transactions on Automatic Control, vol. 57, no. 12, pp. 3169-3174, Dec. 2012. [DOI:10.1109/TAC.2012.2199176]
5. [5] G. Hu, "Robust consensus tracking of a class of second-order multiagent dynamic systems", System Control Letters, vol. 61, no. 1, pp. 134-142, Jan. 2012. [DOI:10.1016/j.sysconle.2011.10.004]
6. [6] H. Zhang and F. L. Lewis, "Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics", Automatica, vol. 48, no. 7, pp. 1432-1439, Jul. 2012. [DOI:10.1016/j.automatica.2012.05.008]
7. [7] R. L. Magin, "Fractional Calculus in Bioengineering", Redding CA, USA: Begell House, 2006.
8. [8] R. Bagley and P. Torvik, "On the fractional calculus model of viscoelastic behavior", Journal of Rheology, vol. 30, pp. 133-155, 1986. [DOI:10.1122/1.549887]
9. [9] I. Cohen, I. Golding, I. G. Ron, and E. Ben-Jacob, "Biofluid dynamics of lubricating bacteria", Mathematics Methods in Applied Sciences, vol. 24, nos. 17-18, pp. 1429-1468, Dec. 2001. [DOI:10.1002/mma.190]
10. [10] Y. Cao, Y. Li, W. Ren, and Y. Chen, "Distributed coordination of networked fractional-order systems", IEEE Transactions on Systems, Man, Cybern. B, Cybern., vol. 40, no. 2, pp. 362-370, Apr. 2010. [DOI:10.1109/TSMCB.2009.2024647]
11. [11] S. G. Samko, A. A. Kilbas, and O. I. Marichev, "Fractional Integrals and Derivatives and Some their Applications", Yverdon, Switzerland: Gordon Breach Sci., 1993.
12. [12] J. Sabatier, O. P. Agrawal, and J. A. T. Machado, "Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering", Heidelberg, Germany: Springer, 2007. [DOI:10.1007/978-1-4020-6042-7]
13. [13] I. Petras, "Fractional-Order Nonlinear Systems", Modeling Analysis and Simulation. New York, NY, USA: Springer, 2011. [DOI:10.1007/978-3-642-18101-6]
14. [14] D. Baleanu, Z. B. Guvenc, and J. A. T. Machado, "New Trends in Nanotechnology and Fractional Calculus Applications", New York, NY, USA: Springer, 2010. [DOI:10.1007/978-90-481-3293-5]
15. [15] S. E. Hamamci, "An algorithm for stabilization of fractional-order time delay systems using fractional-order PID controllers", IEEE Transactions on Automatic Control, vol. 52, no. 10, pp. 1964-1969, Oct. 2007. [DOI:10.1109/TAC.2007.906243]
16. [16] M. A. Duarte-Mermoud, N. Aguila-Camacho, J. A. Gallegos, and R. Castro-Linares, "Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems", Communications in Nonlinear Science and Numerical Simulation, vol. 22, nos. 1-3, pp. 650-659, 2015. [DOI:10.1016/j.cnsns.2014.10.008]
17. [17] W. Sun, Y. Li, C. Li, and Y. Chen, "Convergence speed of a fractional order consensus algorithm over undirected scale-free networks", Asian Journal of Control, vol. 13, no. 6, pp. 936-946, Nov. 2011. [DOI:10.1002/asjc.390]
18. [18] Y. Cao and W. Ren, "Distributed formation control for fractional order systems: Dynamic interaction and absolute/relative damping", System Control Letter, vol. 59, nos. 3-4, pp. 233-240, 2010. [DOI:10.1016/j.sysconle.2010.01.008]
19. [19] Almeida, R., Girejko, E., Hristova, S., & Malinowska, A. B, "Leader-following consensus for fractional multi-agent systems", Advances in Difference Equations, 2019(1), 301, 2019. [DOI:10.1186/s13662-019-2235-9]
20. [20] Ren, G., Yu, Y., Xu, C., & Hai, X, "Consensus of fractional multi-agent systems by distributed event-triggered strategy", Nonlinear Dynamics, 95(1), 541-555, 2019. [DOI:10.1007/s11071-018-4580-8]
21. [21] P. Gong, "Distributed tracking of heterogeneous nonlinear fractional order multi-agent systems with an unknown leader", Journal of Franklin Institute, vol. 354, no. 5, pp. 2226-2244, Mar. 2017. [DOI:10.1016/j.jfranklin.2017.01.001]
22. [22] 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]
23. [23] Wen, G., Zhang, Y., Peng, Z., Yu, Y., & Rahmani, A., "Observer-based output consensus of leader-following fractional-order heterogeneous nonlinear multi-agent systems", International Journal of Control, 1-9, 2019. [DOI:10.1080/00207179.2019.1566636]
24. [24] Sharafian, A., Sharifi, A., & Zhang, W., "Different types of sliding mode controller for nonlinear fractional multi-Agent system", Chaos, Solitons & Fractals, 131, 109481, 2019. [DOI:10.1016/j.chaos.2019.109481]
25. [25] Z.-G. Hou, L. Cheng, and M. Tan, "Decentralized robust adaptive control for the multiagent system consensus problem using neural networks", IEEE Transaction Systems, Man, Cybernetics B, Cybernetics, vol. 39, no. 3, pp. 636-647, Jun. 2009. [DOI:10.1109/TSMCB.2008.2007810]
26. [26] L. Cheng, Z.-G. Hou, M. Tan, Y. Lin, and W. Zhang, "Neural-network based adaptive leader following control for multiagent systems with uncertainties", IEEE Transaction Neural Network, vol. 21, no. 8, pp. 1351-1358, Aug. 2010. [DOI:10.1109/TNN.2010.2050601]
27. [27] A. Das and F. L. Lewis, "Distributed adaptive control for synchronization of unknown nonlinear networked systems", Automatica, vol. 46, no. 12, pp. 2014-2021, Dec. 2010. [DOI:10.1016/j.automatica.2010.08.008]
28. [28] A. Das and F. L. Lewis, "Cooperative adaptive control for synchronization of second-order systems with unknown nonlinearities", International Journal Robust Nonlinear Control, vol. 21, no. 13, pp. 1509-1524, Sep. 2011. [DOI:10.1002/rnc.1647]
29. [29] J. Mei, W. Ren, B. Li, and G. Ma, "Distributed containment control for multiple unknown second-order nonlinear systems with application to networked Lagrangian systems", IEEE Transaction, Neural Network Learn. System, vol. 26, no. 9, pp. 1885-1899, Sep. 2015. [DOI:10.1109/TNNLS.2014.2359955]
30. [30] L. Cheng, M. Cheng, H. Yu, L. Deng, and Z.-G. Hou, "Distributed tracking control of uncertain multiple manipulators under switching topologies using neural networks", In Advances in Neural Networks (LNCS 9719). Cham, Switzerland: Springer, pp. 233-241, Jul. 2016. [DOI:10.1007/978-3-319-40663-3_27]
31. [31] W.G. Kelly, A.C. Peterson, "The Theory of Differential Equations", Springer, Dordrecht, Heidelberg, London, 2010. [DOI:10.1007/978-1-4419-5783-2_1]
32. [32] Podlubny, I, "Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications", Elsevier, (1998).
33. [33] R. Diestel, "Graph Theory", Graduate texts in mathematics, volume 173, no. 7, 2012. [DOI:10.1007/978-3-662-53622-3_7]
34. [34] M. Shahvali, J. Askari, "Cooperative adaptive neural partial tracking errors constrained control for nonlinear multi‐agent systems", International Journal of Adaptive Control and Signal Processing, pp. 1019-1042, 2016. [DOI:10.1002/acs.2657]
Send email to the article author
| Rights and permissions | |
 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |
