Multi-rate sampled-data algorithm for leader–follower flocking

Sahar Yazdani; Mohammad Haeri; Housheng Su

Multi-rate sampled-data algorithm for leader–follower flocking

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Author(s): Sahar Yazdani¹ ; Mohammad Haeri² ; Housheng Su³
- Affiliations: 1: Research Center of Energy and System, Zanjan Branch, Islamic Azad University , Zanjan 45156–58145 , Iran ;
  2: Advanced Control Systems Lab, Electrical Engineering Department , Sharif University of Technology , Tehran 11155–4363 , Iran ;
  3: School of Artificial Intelligence and Automation, Huazhong University of Science and Technology , Luoyu Road 1037, Wuhan 430074 , People's Republic of China
Source: Volume 14, Issue 19, 21 December 2020, p. 3038 – 3046
DOI: 10.1049/iet-cta.2020.0637 , Print ISSN 1751-8644, Online ISSN 1751-8652

Received 24/05/2020, Accepted 18/11/2020, Revised 13/11/2020, Published 25/11/2020

This work presents a new algorithm for flocking with a virtual leader by introducing a new sampling scenario, so-called multi-rate sampling. In the multi-rate sampling, the period of receiving data from different sources is different, but the updating time for all individuals is the same. Here, the authors assume that the period of receiving data from neighbour agents is T , and that from the virtual leader is an integer multiple of it, that is, mT . An upper bound for period T is attained from the upper bound of the energy function that guarantees the neighbouring network to be connected and collision to be avoided between agents. Also, an upper bound on m , which ensures the velocity of informed and uninformed agents to tend the virtual leader's velocity, is derived. The convergence analysis demonstrates that whatever the acquiring period of the virtual leader's information mT is further, then the convergence rate of the group's velocity to the virtual leader's velocity will be greater. Finally, to show the validity of the results, they present a simulation.

References

1. 1)
  - 11. Feng, X., Chen, T.: ‘Sampled-data consensus for multiple double-integrators with arbitrary sampling’, IEEE Trans. Autom. Control, 2012, 57, (12), pp. 3230–3235.
2. 2)
  - 25. Zhang, W.A., Feng, G., Yu, L.: ‘Multi-rate distributed fusion estimation for sensor networks with packet losses’, Automatica, 2012, 48, (9), pp. 2016–2028.
3. 3)
  - 14. Ge, X., Han, Q.L., Ding, D., et al: ‘A survey on recent advances in distributed sampled-data cooperative control of multi-agent systems’, Neurocomputing, 2018, 275, pp. 1684–1701.
4. 4)
  - 23. Chen, T., Qiu, L.: ‘H∞ design of general multi-rate sampled data control systems’, Automatica, 1994, 30, (7), pp. 1139–1152.
5. 5)
  - 21. Wellman, B. J., Hoagg, J.B.: ‘A discrete-time flocking algorithm for agents with sampled-data double-integrator dynamics’. Proc. American Control Conf., Seattle, WA, USA, 2017, pp. 2378–5861.
6. 6)
  - 2. Tanner, H.G., Jadbabaie, A., Pappas, G.J.: ‘Flocking in fixed and switching networks’, IEEE Trans. Autom. Control, 2007, 52, (5), pp. 863–868.
7. 7)
  - 31. Huang, L.: ‘Linear algebra in system and control theory’ (Science Press, Beijing, 1984).
8. 8)
  - 4. Su, H., Wang, X.F, Lin, Z.L.: ‘Flocking for multi-agents with a virtual leader’, IEEE Trans. Autom. Control, 2009, 54, (2), pp. 293–307.
9. 9)
  - 27. Gonzalez, O., Simo, J.C.: ‘On the stability of simplistic and energy-momentum algorithms for non-linear Hamiltonian systems with symmetry’, Comput. Methods Appl. Mech. Eng., 1996, 134, pp. 197–222.
10. 10)
  - 19. Liu, W., Huang, J.: ‘Leader-following consensus for linear multi-agent systems via asynchronous sampled-data control’, IEEE Trans. Autom. Control, 2020, 65, pp. 3215–3222, doi.org/10.1109/TAC.2019.2948256.
11. 11)
  - 16. Tang, Z. J., Huang, T. Z., Shao, J. L., et al: ‘Leader-following consensus for multi-agent system via sampled-data control’, IET Control Theory Appl., 2010, 5, (14), pp. 1658–1665.
12. 12)
  - 5. Su, H., Wang, X.F., Chen, G.: ‘A connectivity-preserving flocking algorithm for multi-agent systems based only on position measurements’, Int. J. Control, 2009, 82, (7), pp. 1334–1343.
13. 13)
  - 3. Olfati-Saber, R.: ‘Flocking for multi-agent dynamic systems: algorithms and theory’, IEEE Trans. Autom. Control, 2006, 51, (3), pp. 401–420.
14. 14)
  - 26. Laila, D. S., Astolfi, A.: ‘Direct discrete-time design for sampled-data Hamiltonian control systems’. 3rd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Nogoya, 2006.
15. 15)
  - 18. Xia, H., Dong, Q.: ‘Dynamic leader-following consensus for asynchronous sampled-data multi-agent systems under switching topology’, Inf. Sci., 2020, 514, pp. 499–511.
16. 16)
  - 15. Cheng, Y., Shi, L., Shao, J., et al: ‘Sampled-data scaled group consensus for second-order multi-agent systems with switching topologies and random link failures’, J. Franklin Inst., 2020, 357, pp. 2868–2881, doi.org/10.1016/j.jfranklin.2019.11.041.
17. 17)
  - 9. Yu, P., Ding, L., Liu, Z.W., et al: ‘Leader-follower flocking based on distributed event-triggered hybrid control’, Int. J. Robust Nonlinear Control, 2016, 26, (1), pp. 143–153.
18. 18)
  - 10. Ghapani, S., Mei, J., Ren, W., et al: ‘Fully distributed flocking with a moving leader for Lagrange networks with parametric uncertainties’, Automatica, 2016, 67, pp. 67–76.
19. 19)
  - 7. Dong, Y., Huang, J.: ‘Flocking with connectivity preservation of multiple double integrator systems subject to external disturbances by a distributed control law’, Automatica, 2015, 55, pp. 197–203.
20. 20)
  - 12. Sun, W., Lu, J., Chen, S., et al: ‘Synchronization of directed coupled harmonic oscillators with sampled-data’, IET Control Theory Appl., 2014, 8, (11), pp. 937–947.
21. 21)
  - 30. Su, H., Chen, G., Wang, X., et al: ‘Adaptive second-order consensus of networked mobile agents with nonlinear dynamics’, Automatica, 2011, 47, (2), pp. 368–375.
22. 22)
  - 8. Yazdani, S., Haeri, M.: ‘Distributed observer type protocol for flocking of linear second-order multi-agent systems subject to external disturbance’, J. Dyn. Syst., Meas., Control, 2019, 141, (6), pp. 061004–061011.
23. 23)
  - 1. Reynolds, C.W.: ‘Flocks, herds, and schools: a distributed behavioral model’, Comput. Graph., 1987, 21, (4), pp. 25–34.
24. 24)
  - 24. Ritchey, V.S., Franklin, G.F.: ‘A stability criterion for asynchronous multi-rate linear systems’, IEEE Trans. Autom. Control, 1989, 34, pp. 1529–1535.
25. 25)
  - 17. Ajwad, S. A., Ménard, T., Moulay, T., et al: ‘Observer based leader-following consensus of second-order multi-agent systems with nonuniform sampled position data’, J. Franklin Inst., 2019, 356, (16), pp. 10031–10057.
26. 26)
  - 13. Chen, F., Yu, H., Xia, X.: ‘Output consensus of multi-agent systems with delayed and sampled-data’, IET Control Theory Appl., 2017, 11, (5), pp. 632–639.
27. 27)
  - 29. Merris, R.: ‘Laplacian matrices of graph: a survey’, Linear Algebr. Appl., 1994, 197–198, pp. 143–176.
28. 28)
  - 28. Yalçın, Y., Gören-Sümer, L.: ‘Direct discrete-time control of port controlled Hamiltonian systems’, Turkish J. Electr. Eng. Comput. Sci., 2010, 18, pp. 913–924.
29. 29)
  - 22. Yazdani, S., Haeri, M.: ‘Sampled-data leader–follower algorithm for flocking of multi-agent systems’, IET Control Theory Appl., 2019, 13, (5), pp. 609–619.
30. 30)
  - 20. Han, F., Gao, L., Yang, H.: ‘Sampling control on collaborative flocking motion of discrete-time system with time-delays’, Neorocomputing, 2019, 216, pp. 242–249.
31. 31)
  - 6. Wen, G., Duan, Z., Su, H., et al: ‘A connectivity-preserving flocking algorithm for multi-agent dynamical systems with bounded potential function’, IET Control Theory Appl., 2012, 6, (6), pp. 813–821.

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