Synchronization of the chaotic fractional-order multi-agent systems under partial contraction theory

[1] B. Bandyopadhyay, S. Kamal, Stabilization and Control of Fractional Order Systems a Sliding
Mode Approach, Switzerland: Springer International Publishing, 2015.
[2] B. Blasius, A. Huppert, L. Stone, Complex dynamics and phase synchronization in spatially ex-
tended ecological systems, Nature 399 (1999) 354–359.
[3] Y. Cao, Y. Li, W. Ren, Y. Chen, Distributed coordination of networked fractional-order systems,
IEEE Trans. on Sys., Man, and Cyber., Part B (Cyber.) 40 (2009) 362–370.
[4] Y. Cao, W. Ren, Z. Meng, Decentralized finite-time sliding mode estimators and their applications
indecentralized finite-time formation tracking, Syst. Control Lett. 59 (2010) 522–529.
[5] C. Y. Chee, D. Xu, Secure digital communication using controlled projective synchronisation of
chaos, Chaos Solit. Fractals 23 (2005) 1063–1070.
[6] S.-J. Chung, Nonlinear Control and Synchronization of Multiple Lagrangian Systems with Appli-
cation to Tethered Formation Flight Spacecraft, PhD thesis, Massachusetts Institute of Technology,
2007.
[7] L.L. Gonz`alez-Romeo, R. Reyes-B`aez, J.F. Guerrero-Castellanos, B. Jayawardhana, J.J. Cid- Mon-
jaraz, O. G. F`elix-Beltr´an, Contraction-based nonlinear controller for a laser beam stabilization
system using a variable gain, IEEE Control Syst. Lett. 5 (2020) 761–766.

[8] G. Liu, Q. Sun, R. Wang, Y. Huang , Reduced-order observer-based fuzzy adaptive dynamic event-
triggered consensus control for multi-agent systems with communication faults, Nonlinear Dyn.
110 (2022) 1421–1435.
[9] G. Jing, Y. Zheng, L. Wang, Flocking of multi-agent systems with multiple groups, Int. J. Control
87 (2014) 2573–2582.
[10] S. Kamal, B. Bandyopadhyay, S. Spurgeon, Stabilization of a fractional-order chain of integrators:
a contraction-based approach, IMA J. Math. Control Inf. 32 (2015) 291–303.
[11] A. Kilbas, Theory and Applications of Fractional Differential Equations, Elsevier, 2009.
[12] M. Lakshmanan, K. Murali, Chaos in Nonlinear Oscillators: Controlling and Synchronization, 13,
World scientific, 1996.
[13] C. Li, C. Tao, On the fractional adams method, Comput. Math. Appl. 58 (2009) 1573–1588.
[14] W. Liu, S. Zhou, Y. Qi, X. Wu, Leaderless consensus of multi-agent systems with Lipschitz nonlin-
ear dynamics and switching topologies, Neurocomputing 173 (2016) 1322–1329.
[15] J.G. Lu, Chaotic dynamics of the fractional-order l¨u system and its synchronization, Phys. Lett. A
354 (2006) 305–311.
[16] M.Sader, W. Li, Z. Liu, H. Jiang, C. Shang, Semi-global fault-tolerant cooperative output regulation
of heterogeneous multi-agent systems with actuator saturation, Inf. Sci. 641 (2023) 119028.
[17] N.A. Zabidi, Z.A. Majid, A. Kilicman, F. Rabiei, Numerical solutions of fractional differential
equations by using fractional explicit adams method, Math. 8 (2020) 1–23.
[18] L.M. Pecora, T.L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett. 64 (1990) 821.
[19] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
[20] A. Ruzitalab, M.H. Farahi, G. Erjaee, Partial contraction analysis of coupled fractional order sys-
tems, J. Appl. Math. 2018 (2018).
[21] L.-J. Sheu, H.-K. Chen, J.-H. Chen, L.-M. Tam, W.-C. Chen, K.-T. Lin, Y. Kang, Chaos in the
Newton-Leipnik system with fractional order, Chaos Solit. Fractals 36 (2008) 98–103.
[22] W. Wang, J.-J. E. Slotine, On partial contraction analysis for coupled nonlinear oscillators, Biol.
Cybern. 92 (2005) 38–53.
[23] M. Wooldridge, An Introduction to Multiagent Systems, John Wiley & Sons , 2009.
[24] C.W. Wu, L.O. Chua, A simple way to synchronize chaotic systems with applications to secure
communication systems, Int. J. Bifurcat. Chaos 3 (1993) 1619–1627.
[25] Z. Yu, H. Jiang, C. Hu, Leader-following consensus of fractional-order multi-agent systems under
fixed topology, Neurocomputing 149 (2015) 613–620.