access icon free Second-order controllability of two-time-Scale discrete-time multi-agent systems

© The Institution of Engineering and Technology
Received 02/03/2019, Accepted 24/06/2019, Revised 12/06/2019, Published 25/06/2019

In this study, the controllability of multi-agent systems with second-order dynamic under discrete-time model, which evolve on two time scales. The authors first characterise the systems by difference equations with a singular perturbation parameter. Then, in order to get rid of the singular perturbation parameter, they split the systems into a slow subsystem and fast subsystem based on the iterative method and approximate approach. Moreover, according to matrix theory, they deduce a lot of necessary and/or sufficient controllability criteria of the systems. In particular, a second-order controllability criterion only depending on the eigenvalues of matrices is proposed, which is more easy-to-use and efficient. A simulation example is lastly given to clarify the validity of all theoretical results.

Inspec keywords: iterative methods; eigenvalues and eigenfunctions; discrete time systems; matrix algebra; singularly perturbed systems; multi-agent systems

Other keywords: time scales; sufficient controllability criteria; second-order controllability criterion; two-time-Scale discrete-time multiagent systems; necessary controllability criteria; singular perturbation parameter; discrete-time model; / controllability criteria

Subjects: Control system analysis and synthesis methods; Discrete control systems; Algebra; Optimal control

References

    1. 1)
      • 15. Su, H., Ye, Y., Qiu, Y., et al: ‘Semi-global output consensus for discrete-time switching networked systems subject to input saturation and external disturbances’, IEEE Trans. Cybern., 2019, 49, (11), pp. 3934–3945.
    2. 2)
      • 13. Rong, Z., Wu, Z., Hao, D., et al: ‘Diversity of timescale promotes the maintenance of extortioners in a spatial prisoner's dilemma game’, New J. Phys., 2015, 17, p. 033032.
    3. 3)
      • 44. Jihene, B., Irinel-Constantin, M., Jamal, D.: ‘Synchronization in networks of linear singularly perturbed systems’. American Control Conf., Boston, USA, 2016, pp. 4293–4298.
    4. 4)
      • 1. Xu, X., Rong, Z., Tian, Z., et al: ‘Timescale diversity facilitates the emergence of cooperation-extortion alliances in networked systems’, Neurocomputing, 2019, 350, pp. 195–201.
    5. 5)
      • 50. Su, H., Long, M., Zeng, Z.: ‘Controllability of two-time-scale discrete-time multi-agent systems’, IEEE Trans. Cybern., 2018, pp. 1–10, doi: 10.1109/TCYB.2018.2884498.
    6. 6)
      • 51. Long, M., Su, H., Wang, X., et al: ‘Controllability of heterogeneous multiagent systems with two-time-scale feature’, Chaos, 2019, 29, p. 043116.
    7. 7)
      • 30. Jiang, F., Wang, L., Xie, G., et al: ‘On the controllability of multiple dynamic agents with fixed topology’. American Control Conf., St. Louis, USA, 2009, pp. 5665–5670.
    8. 8)
      • 25. Tanner, H.: ‘On the controllability of nearest neighbor interconnections’. IEEE Conf. on Decision Control, Nassau, Bahamas, 2004, pp. 2467–2472.
    9. 9)
      • 46. Litkouhi, B., Khalil, H.: ‘Multirate and composite control of two-time-scale discrete-time systems’, IEEE Trans. Autom. Control, 2003, 30, (7), pp. 645–651.
    10. 10)
      • 52. Kokotovic, P.V., O'Malley, R.E.Jr., Sannuti, P.: ‘Singular perturbation and order reduction in control theory-an overview’, Automatica, 1976, 12, (2), pp. 123–132.
    11. 11)
      • 23. Liu, P., Zeng, Z., Wang, J.: ‘Multistability analysis of a general class of recurrent neural networks with non-monotonic activation functions and time-varying delays’, Neural Netw., 2016, 79, pp. 117–127.
    12. 12)
      • 40. Liu, B., Han, Y., Jiang, F., et al: ‘Group controllability of discrete-time multi-agent systems’, J. Franklin Inst., 2016, 353, (14), pp. 3524–3559.
    13. 13)
      • 4. Wang, X., Su, H.: ‘Consensus of hybrid multi-agent systems by event-triggered/self-triggered strategy’, Appl. Math. Comput., 2019, 359, pp. 490–501.
    14. 14)
      • 47. Kokotovic, P., Khalil, H., O'Reilly, J.: ‘Singular perturbation methods in control analysis and design’ (SIAM, Philadephia, 1999).
    15. 15)
      • 31. Wang, L., Jiang, F., Xie, G., et al: ‘Controllability of multi-agent systems based on agreement protocols’, Science China, 2009, 52, (11), pp. 2074–2088.
    16. 16)
      • 43. Meyer-Bäse, A., Ohl, F., Scheich, H.: ‘Singular perturbation analysis of competitive neural networks with different time scales’, Neural Comput., 1996, 8, (8), pp. 1731–1742.
    17. 17)
      • 53. Saksena, V.R., O'Reilly, J., Kokotovic, P.V.: ‘Singular perturbations and time-scale methods in control theory-a survey 1976-1983’, Automatica, 1984, 20, (3), pp. 273–293.
    18. 18)
      • 41. Liu, B., Su, H., Jiang, F., et al: ‘Group controllability of continuous-time multi-agent systems’, IET Control Theory Applic., 2018, 12, (11), pp. 1665–1671.
    19. 19)
      • 36. Ji, Z., Lin, H., Yu, H.: ‘Leaders in multi-agent controllability under consensus algorithm and tree topology’, Syst. Control Lett., 2012, 61, (9), pp. 918–925.
    20. 20)
      • 11. Su, H., Sun, Y., Zeng, Z.: ‘Semi-global observer-based nonnegative edge consensus of networked systems with actuator saturation’, IEEE Trans. Cybern., 2019, pp. 1–10, doi: 10.1109/TCYB.2019.2917006.
    21. 21)
      • 14. Sun, Y., Su, H., Wang, X., et al: ‘Semi-global edge-consensus of linear discrete-time multi-agent systems with positive constraint and input saturation’, IET Control Theory Applic., 2019, 13, (7), pp. 979–987.
    22. 22)
      • 20. Su, H., Chen, M.Z.Q.: ‘Multi-agent containment with input saturation on switching topologies’, IET Control Theory Applic., 2015, 9, (3), pp. 399–409.
    23. 23)
      • 49. Long, M., Su, H., Liu, B.: ‘Second-order controllability of two-time-scale multi-agent systems’, Appl. Math. Comput., 2019, 343, pp. 299–313.
    24. 24)
      • 39. Yu, J., Wang, L.: ‘Group consensus of multi-agent systems with undirected communication graphs’. Proc. of the 7th Asian Control Conf., Hong Kong, 2009, pp. 105–110.
    25. 25)
      • 9. Su, H., Wu, H., Lam, J.: ‘Positive edge-consensus for nodal networks via output feedback’, IEEE Trans. Autom. Control, 2019, 64, (3), pp. 1244–1249.
    26. 26)
      • 8. Su, H., Wu, H., Chen, X., et al: ‘Positive edge consensus of complex networks’, IEEE Trans. Syst. Man Cybern., Syst., 2018, 48, (12), pp. 2242–2250.
    27. 27)
      • 17. Wu, H., Su, H.: ‘Observer-based consensus for positive multiagent systems with directed topology and nonlinear control input’, IEEE Trans. Syst. Man Cybern., Syst., 2019, 49, (7), pp. 1459–1469.
    28. 28)
      • 28. Liu, B., Su, H., Li, R., et al: ‘Switching controllability of discrete-time multi-agent systems with multiple leaders and time-delays’, Appl. Math. Comput., 2014, 228, (9), pp. 571–588.
    29. 29)
      • 26. Liu, B., Chu, T., Wang, L., et al: ‘Controllability of switching networks of multi-agent systems’, Int. J. Robust Nonlinear Control, 2012, 22, (6), pp. 630–644.
    30. 30)
      • 12. Su, H., Wu, H., Chen, X.: ‘Observer-based discrete-time nonnegative edge synchronization of networked systems’, IEEE Trans. Neural Netw. Learn. Syst., 2017, 28, (10), pp. 2446–2455.
    31. 31)
      • 5. Zhang, Y., Li, H., Sun, J., et al: ‘Cooperative adaptive event-triggered control for multi-agent systems with actuator failures’, IEEE Trans. Syst. Man Cybern., Syst., 2019, pp. 1–10, doi: 10.1109/TCYB.2019.2893645.
    32. 32)
      • 34. Rahimian, M.A., Aghdam, A.G.: ‘Structural controllability of multi-agent networks: robustness against simultaneous failures’, Automatica, 2013, 49, (11), pp. 3149–3157.
    33. 33)
      • 24. Su, H., Zhang, J., Chen, X.: ‘A stochastic sampling mechanism for time-varying formation of multiagent systems with multiple leaders and communication delays’, IEEE Trans. Neural Netw. Learn. Syst., 2019, pp. 1–9, doi: 10.1109/TNNLS.2019.2891259.
    34. 34)
      • 33. Ji, Z., Yu, H.: ‘A new perspective to graphical characterization of multi-agent controllability’, IEEE Trans. Cybern., 2017, 47, (6), pp. 1471–1483.
    35. 35)
      • 35. Parlangeli, G., Notarstefano, G.: ‘On the reachability and observability of path and cycle graphs’, IEEE Trans. Autom. Control, 2012, 57, (3), pp. 743–748.
    36. 36)
      • 29. Liu, B., Feng, H., Wang, L., et al: ‘Controllability of second-order multiagent systems with multiple leaders and general dynamics’, Math. Probl. Eng., 2013, 2013, (4), pp. 14–26.
    37. 37)
      • 19. Mao, Y., Xu, X., Rong, Z., et al: ‘The emergence of cooperation-extortion alliance on scale-free networks with normalized payoff’, Europhys. Lett. (EPL), 2018, 122, p. 50005.
    38. 38)
      • 6. Su, H., Liu, Y., Zeng, Z.: ‘Second-order consensus for multiagent systems via intermittent sampled position data control’, IEEE Trans. Cybern., 2019, pp. 1–10, doi: 10.1109/TCYB.2018.2879327.
    39. 39)
      • 27. Liu, B., Chu, T., Wang, L., et al: ‘Controllability of a leader-follower dynanic network with switching topology’, IEEE Trans. Autom. Control, 2008, 53, (4), pp. 1009–1013.
    40. 40)
      • 22. Liu, P., Zeng, Z., Wang, J.: ‘Multiple Mittag–Leffler stability of fractional-order recurrent neural networks’, IEEE Trans. Syst. Man Cybern., Syst., 2017, 47, (8), pp. 2279–2288.
    41. 41)
      • 32. Rahmani, A., Ji, M., Mesbahi, M., et al: ‘Controllability of multi-agent systems from a graph theoretic perspective’, SIAM J. Control Optim., 2009, 48, (1), pp. 162–186.
    42. 42)
      • 37. Notarstefano, G., Parlangeli, G.: ‘Controllability and observability of grid graphs via reduction and symmetries’, IEEE Trans. Autom. Control, 2013, 58, (7), pp. 1719–1731.
    43. 43)
      • 48. Long, M., Su, H., Liu, B.: ‘Group controllability of two-time-scale multi-agent networks’, J. Franklin Inst., 2018, 355, (13), pp. 6045–6061.
    44. 44)
      • 2. Su, H., Deng, C., Guo, F., et al: ‘Distributed load sharing and transmission power loss optimization for DC microgrids’, IET Control Theory Applic., 2018, doi: 10.1049/iet-cta.2018.5678.
    45. 45)
      • 45. Balldes, M., Daoutidis, P.: ‘Control of integrated process networks-A multi-time scale perspective’, Comput. Chem. Eng., 2005, 31, (5), pp. 426–444.
    46. 46)
      • 42. Al-Ashoor, R., Khorasani, K.: ‘A decentralized indirect adaptive control for a class of two-time-scale nonlinear systems with application to flexible-joint manipulators’, IEEE Trans. Ind. Electon., 2002, 46, (5), pp. 1019–1029.
    47. 47)
      • 3. Liang, H., Zhang, Y., Huang, T., et al: ‘Prescribed performance cooperative control for multi-agent systems with unknown control directions and input quantization’, IEEE Trans. Cybern., 2019, pp. 1–10, doi: 10.1109/TCYB.2019.2893645.
    48. 48)
      • 7. Wang, X., Su, H.: ‘Self-triggered leader-following consensus of multi-agent systems with input time delay’, Neurocomputing, 2019, 330, pp. 70–77.
    49. 49)
      • 16. Liang, H., Zhang, Z., Ahn, C.K.: ‘Event-triggered fault detection and isolation of discrete-time systems based on geometric technique’, IEEE Trans. Circuits Syst. II, Express Briefs, 2019, pp. 1–1, doi: 10.1109/TCSII.2019.2907706.
    50. 50)
      • 38. Su, H., Chen, M.Z.Q., Wang, X., et al: ‘Adaptive cluster synchronization of coupled harmonic oscillators with multiple leaders’, IET Control Theory Applic., 2013, 7, (5), pp. 765–772.
    51. 51)
      • 10. Wu, H., Su, H.: ‘Discrete-time positive edge-consensus for undirected and directed nodal networks’, IEEE Trans. Circuits Syst.-II, Express Briefs, 2018, 65, (2), pp. 221–225.
    52. 52)
      • 21. Zhang, J., Su, H.: ‘Time-varying formation for linear multi-agent systems based on sampled data with multiple leaders’, Neurocomputing, 2019, 339, pp. 59–65.
    53. 53)
      • 18. Su, H., Ye, Y., Chen, X., et al: ‘Necessary and sufficient conditions for consensus in fractional-order multiagent systems via sampled data over directed graph’, IEEE Trans. Syst. Man Cybern., Syst., 2019, pp. 1–11, doi: 10.1109/TSMC.2019.2915653.
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