Cluster consensus of general fractional-order nonlinear multi agent systems via adaptive sliding mode controller

• Autorzy: Yaghoubi Zahra , Talebi Heidar Ali

Identyfikatory

DOI

10.24425/acs.2019.131230

• Języki publikacji: EN

Abstrakty

EN

In this paper cluster consensus is investigated for general fractional-order multi agent systems with nonlinear dynamics via adaptive sliding mode controller. First, cluster consensus for fractional-order nonlinear multi agent systems with general form is investigated. Then, cluster consensus for the fractional-order nonlinear multi agent systems with first-order and general form dynamics is investigated by using adaptive sliding mode controller. Sufficient conditions for achieving cluster consensus for general fractional-order nonlinear multi agent systems are proved based on algebraic graph theory, Lyapunov stability theorem and Mittag-Leffler function. Finally, simulation examples are presented for first-order and general form multi agent systems, i.e. a single-link flexible joint manipulator which demonstrates the efficiency of the proposed adaptive controller.

Słowa kluczowe

EN

nonlinear multi agent systems; cluster consensus; fractional-order systems; adaptive sliding mode controller

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2019
• Tom: Vol. 29, No. 4
• Strony: 643--665
• Opis fizyczny: Bibliogr. 31 poz., rys., tab., wykr., wzory

Twórcy

autor

Yaghoubi Zahra

• Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran.

autor

Talebi Heidar Ali

• Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran

Bibliografia

• [1] N. Aguila-Camacho, M. A. Duarte-Mermoud and J. A. Gallegos: Lyapunov functions for fractional order systems. Communications in Nonlinear Science and Numerical Simulation, 19(9), (2014), 2951–2957.
• [2] Y. Cao, Y. Li, W. Ren and Y. Chen: Distributed coordination of networked fractional-order systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 40(2), (2010), 362–370.
• [3] B. Das, B. Subudhi and B. B. Pati: Adaptive sliding mode formation control of multiple underwater robots. Archives of Control Sciences, 24(4), (2014), 515–543.
• [4] L. Ding, P. Yu, Z.-W. Liu and Z.-H. Guan: Consensus and performance optimisation of multi-agent systems with position-only information via impulsive control. IET Control Theory & Applications, 7(1), (2013), 16–24.
• [5] S. El-Ferik, A. Qureshi and F. L. Lewis: Neuro-adaptive cooperative tracking control of unknown higher-order affine nonlinear systems. Automatica, 50(3), (2014), 798–808.
• [6] P. Gong: Distributed consensus of non-linear fractional-order multi-agent systems with directed topologies. IET Control Theory & Applications, 10(18), (2016), 2515–2525.
• [7] P. Gong: Distributed tracking of heterogeneous nonlinear fractional-order multi-agent systems with an unknown leader. Journal of the Franklin Institute, 354(5), (2017), 2226–2244.
• [8] R. A. Horn and C. R. Johnson: Matrix Analysis. Cambridge University Press, 1990.
• [9] T. Kaczorek: A new method for computation of positive realizations of fractional linear continuous-time systems. Archives of Control Sciences, 28(4), (2018), 511–525.
• [10] Y. Li, Y. Chen and I. Podlubny: Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability. Computers & Mathematics with Applications, 59(5), (2010), 1810–1821.
• [11] Y. Li, Y. Huang, P. Lin and W. Ren: Distributed rotating consensus of second-order multi-agent systems with nonuniform delays. Systems & Control Letters, 117 (2018), 18–22.
• [12] Z. Li, Z. Duan, G. Chen and L. Huang: Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint. IEEE Transactions on Circuits & Systems I: Regular Papers, 57(1), (2010), 213–224.
• [13] Z. Li, X. Liu, P. Lin and W. Ren: Consensus of linear multi-agent systems with reduced-order observer-based protocols. Systems & Control Letters, 60(7), (2011), 510–516.
• [14] Z. Li, W. Ren, X. Liu and M. Fu: Consensus of multi-agent systems with general linear and Lipschitz nonlinear dynamics using distributed adaptive protocols. IEEE Transactions on Automatic Control, 58(7), (2013), 1786–1791.
• [15] J. Liang-Hao and L. Xiao-Feng: Consensus problems of first-order dynamic multi-agent systems with multiple time delays. Chinese Physics B, 22(4), (2013), 040203.
• [16] C.-Q. Ma and J.-F. Zhang: Necessary and sufficient conditions for consensusability of linear multi-agent systems. IEEE Transactions on Automatic Control, 55(5), (2010), 1263–1268.
• [17] J. Mei, W. Ren and J. Chen: Distributed consensus of second-order multiagent systems with heterogeneous unknown inertias and control gains under a directed graph. IEEE Transactions on Automatic Control, 61(8), (2016), 2019–2034.
• [18] R. Olfati-Saber and R. M. Murray: Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 49(9), (2004), 1520–1533.
• [19] I. Podlubny: Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Elsevier 1998.
• [20] W. Ren and R. W. Beard: Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control, 50(5), (2005), 655–661.
• [21] F. Shamsi, H. A. Talebi and F. Abdollahi: Output consensus control of multi-agent systems with nonlinear non-minimum phase dynamics. International Journal of Control, 91(4), (2018), 785–796.
• [22] Y. Shang: Group consensus in generic linear multi-agent systems with intergroup non-identical inputs. Cogent Engineering, 1(1), (2014), 947761.
• [23] G. Wen, Z. Duan, G. Chen and W. Yu: Consensus tracking of multi-agent systems with Lipschitz-type node dynamics and switching topologies. IEEE Transactions on Circuits and Systems I: Regular Papers, 61(2), (2014), 499–511.
• [24] Z. Yaghoubi and H. A. Talebi: Consensus tracking for nonlinear fractional order multi agent systems using adaptive sliding mode controller. Mechatronic Systems and Control (formerly Control and Intelligent Systems), 47(4), (2019), 194–200.
• [25] X. Yang, C. Li, T. Huang and Q. Song: Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses. Applied Mathematics and Computation, 293 (2017), 416–422.
• [26] S. J. Yoo: Distributed adaptive containment control of uncertain nonlinear multi-agent systems in strict-feedback form. Automatica, 49(7), (2013), 2145–2153.
• [27] W. Yu, W. Ren, W. X. Zheng, G. Chen and J. Lu: Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics. Automatica, 49(7), (2013), 2107–2115.
• [28] W. Yu, Y. Li, G. Wen, X. Yu and J. Cao: Observer design for tracking consensus in second-order multi-agent systems: Fractional order less than two. IEEE Transactions on Automatic Control, 62(2), (2017), 894–900.
• [29] J. Zhan and X. Li: Cluster consensus in networks of agents with weighted cooperative–competitive interactions. IEEE Transactions on Circuits & Systems II: Express Briefs, 65(2), (2018), 241–245.
• [30] S. Zhang, Y. Yu and J. Yu: LMI conditions for global stability of fractional order neural networks. IEEE transactions on neural networks and learning systems, 28(10), (2017), 2423–2433.
• [31] F. Zhu and Z. Han: A note on observers for Lipschitz nonlinear systems. IEEE Transactions on Automatic Control, 47(10), (2002), 1751–1754.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).