Consensus in second-order multi-agent systems via impulsive control using position-only information with heterogeneous delays

Yan-Wu Wang; Jing-Wen Yi

Consensus in second-order multi-agent systems via impulsive control using position-only information with heterogeneous delays

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Author(s): Yan-Wu Wang ^{1, 2} and Jing-Wen Yi ^{1, 2}
- Affiliations: 1: School of Automation, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China;
  2: Key Laboratory of Image Processing and Intelligent Control (Huazhong University of Science and Technology), Ministry of China
Source: Volume 9, Issue 3, 05 February 2015, p. 336 – 345
DOI: 10.1049/iet-cta.2014.0425 , Print ISSN 1751-8644, Online ISSN 1751-8652

Received 23/04/2014, Accepted 20/08/2014, Revised 24/07/2014, Published 19/12/2014

This study investigates the consensus problem of second-order multi-agent systems (MASs) via impulsive control using position-only information with communication delays. The communication delays between any two distinct agents are different which can be larger than one impulsive period. A distributed impulsive consensus protocol is designed, in which only the delayed sampled relative positions to neighbours and the relative position to the last sampling state are utilised. By introducing some virtual subgraphs and performing three steps of model transformation, the consensus problem of original continuous-time system is converted to the stability problem of a discrete-time expanded error system. Some necessary and sufficient criteria are derived to grantee the dynamic average-consensus of the MAS. Furthermore, a special case, that is, the delays less than one impulsive period, is discussed, and the bounds of impulsive periods for the dynamic average-consensus are obtained in explicit expressions for both the undirected and directed communication graphs, respectively. Two numerical simulation examples are given to illustrate the effectiveness of theoretical results.

References

1. 1)
  - T. Li , J. Zhang . Sampled-data based average consensus with measurement noises: convergence analysis and uncertainty principle. Sci. China Ser. F , 11 , 2089 - 2103
2. 2)
  - 21. Han, X., Lu, J.-A., Wu, X.: ‘Synchronization of impulsively coupled systems’, Int. J. Bifurcation Chaos, 2008, 18, (05), pp. 1539–1549 (doi: 10.1142/S0218127408021154).
3. 3)
  - 14. Chen, W., Li, X.: ‘Observer-based consensus of second-order multi-agent system with fixed and stochastically switching topology via sampled data’, Int. J. Robust Nonlinear Control, 2014, 24, (3), pp. 567–584 (doi: 10.1002/rnc.2906).
4. 4)
  - J.H. Seo , J. Back , H. Kim , H. Shim . Output feedback consensus for high-order linear systems having uniform ranks under switching topology. IET Control Theory Appl. , 8 , 1118 - 1124
5. 5)
  - Z.W. Liu , Z.H. Guan , X.M. Shen , G. Feng . Consensus of multi-agent networks with aperiodic sampled communication via impulsive algorithm using position-only measurements. IEEE Trans. Autom. Control , 10 , 2639 - 2643
6. 6)
  - W.W. Yu , W.X. Zheng , G.R. Chen , W. Ren , J.D. Cao . Second-order consensus in multi-agent dynamical systems with sampled position data. Automatica , 7 , 1496 - 1503
7. 7)
  - 22. Jiang, H., Bi, Q.: ‘Impulsive synchronization of networked nonlinear dynamical systems’, Phys. Lett. A, 2010, 374, (27), pp. 2723–2729 (doi: 10.1016/j.physleta.2010.04.063).
8. 8)
  - A. Kashyap , T. Basar , R. Srikant . Quantized consensus. Automatica , 6 , 1192 - 1203
9. 9)
  - 28. Bullo, F., Cortés, J., Martınez, S.: ‘Distributed control of robotic networks’ Applied Mathematics Series (Princeton University Press, 2009).
10. 10)
  - T. Li , M. Fu , L. Xie , J. Zhang . Distributed consensus with limited communication date rate. IEEE Trans. Autom. Control , 2 , 279 - 291
11. 11)
  - R. Olfati-Saber . Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Autom. Control , 3 , 401 - 420
12. 12)
  - H. Qing , M.H. Wassim , P.B. Sanjay . On robust control algorithms for nonlinear network consensus protocols. Int. J. Robust Nonlinear Control , 3 , 269 - 284
13. 13)
  - R. Olfati-Saber , R.M. Murray . Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control , 9 , 1520 - 1533
14. 14)
  - H. Liu , G. Xie , L. Wang . Necessary and sufficient conditions for solving consensus problems of double-integrator dynamics via sampled control. Int. J. Robust Nonlinear Control , 15 , 1706 - 1722
15. 15)
  - S. Liu , L. Xie , H. Zhang . Distributed consensus for multi-agent systems with delays and noises in transmission channels. Automatica , 920 - 934
16. 16)
  - 23. Zhang, Q., Chen, S., Yu, C.: ‘Impulsive consensus problem of second-order multi-agent systems with switching topologies’, Commun. Nonlinear Sci. Numer. Simul., 2012, 17, (1), pp. 9–16 (doi: 10.1016/j.cnsns.2011.04.007).
17. 17)
  - 23. Jiang, H., Yu, J., Zhou, C.: ‘Consensus of multi-agent linear dynamic systems via impulsive control protocols’, Int. J. Syst. Sci., 2011, 42, (6), pp. 967–976 (doi: 10.1080/00207720903267866).
18. 18)
  - 4. Ding, L., Yu, P., Liu, Z.W., Guan, Z.H.: ‘Consensus and performance optimisation of multi-agent systems with position-only information via impulsive control’, IET Control Theory Appl., 2013, 7, (1), pp. 16–24 (doi: 10.1049/iet-cta.2012.0461).
19. 19)
  - 11. Xiong, W., Ho, D., Cao, J.: ‘Impulsive consensus of multi-agent directed networks with nonlinear perturbations’, Int. J. Robust Nonlinear Control, 2012, 22, (14), pp. 1571–1582 (doi: 10.1002/rnc.1768).
20. 20)
  - 19. Ding, L., Yu, P., Liu, Z.-W., Guan, Z.-H., Feng, G.: ‘Consensus of second-order multi-agent systems via impulsive control using sampled hetero-information’, Automatica, 2013, 49, (9), pp. 2881–2886 (doi: 10.1016/j.automatica.2013.06.014).
21. 21)
  - 12. Cao, Y., Ren, W.: ‘Distributed coordinated tracking with reduced interaction via a variable structure approach’, IEEE Trans. Autom. Control, 2012, 57, (1), pp. 33–48 (doi: 10.1109/TAC.2011.2146830).
22. 22)
  - L. Moreau . Stability of multi-agent systems with time-dependent communication links. IEEE Trans. Autom. Control , 2 , 169 - 182
23. 23)
  - 26. Yu, W., Zhou, L., Yu, X., Lv, J., Lu, R.: ‘Consensus in multi-agent systems with second-order dynamics and sampled data’, IEEE Trans. Ind. Inf., 2013, 9, (4), pp. 2137–2146 (doi: 10.1109/TII.2012.2235074).
24. 24)
  - J. Hu , Y.S. Lin . Consensus control for multi-agent systems with double-integrator dynamics and time delays. IET Control Theory Appl. , 109 - 118
25. 25)
  - 30. Wang, L., Huang, L., Hollot, C.: ‘On the robust stability of polynomials and related topics’, J. Syst. Sci. Complex., 1992, 5, (1), pp. 42–54.
26. 26)
  - 29. Ogata, K.: ‘Discrete-time control systems’ vol. 8 (Prentice-Hall, Englewood Cliffs, NJ, 1995).
27. 27)
  - 34. Gantmakher, F.R.: ‘The theory of matrices’ (American Mathematical Soc., 1959).
28. 28)
  - 33. Parks, P.C., Hahn, V.: ‘Stability theory’ (Prentice-Hall, New York, 1993).
29. 29)
  - 35. Horn, R.A., Johnson, C.R.: ‘Matrix analysis’ (Cambridge University Press, New York, 1985).
30. 30)
  - J.A. Fax , R.M. Murray . Information flow and cooperative control of vehicle formations. IEEE Trans. Autom. Control , 9 , 1465 - 1476
31. 31)
  - 32. Ren, W., Cao, Y.: ‘Distributed coordination of multi-agent networks: emergent problems, models, and issues’ (Springer-Verlag, London, 2010).
32. 32)
  - M. Huang , J.H. Manton . Coordination and consensus of networked agents with noisy measurements: stochastic algorithms and asymptotic behavior. SIAM J. Control Optim. , 1 , 134 - 161
33. 33)
  - 15. Cheng, L., Wang, Y., Hou, Z.-G., Tan, M., Cao, Z.: ‘Sampled-data based average consensus of second-order integral multi-agent systems: switching topologies and communication noises’, Automatica, 2013, 49, (5), pp. 1458–1464 (doi: 10.1016/j.automatica.2013.02.004).
34. 34)
  - Z.Y. Lin , B. Francis , M. Maggiore . State agreement for continuous-time coupled nonlinear systems. SIAM J. Control Optim. , 1 , 288 - 307
35. 35)
  - Z.H. Guan , Z.W. Liu , G. Feng , M. Jian . Impulsive consensus algorithms for the second-order multi-agent networks with sampled information. Automatica , 7 , 1397 - 1404

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Consensus in second-order multi-agent systems via impulsive control using position-only information with heterogeneous delays

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