access icon free Decentralised adaptive control of a class of hidden leader–follower non-linearly parameterised coupled MASs

In this study, decentralised adaptive control is investigated for a class of discrete-time non-linear hidden leader–follower multi-agent systems (MASs). Different from the conventional leader–follower MAS, among all the agents, there exists a hidden leader that knows the desired reference trajectory, while the follower agents know neither the desired reference signal nor which is a leader agent. Each agent is affected from the history information of its own neighbours. The dynamics of each agent is described by the non-linear discrete-time auto-regressive model with unknown parameters. In order to deal with the uncertainties and non-linearity, a projection algorithm is applied to estimate the unknown parameters. Based on the certainty equivalence principle in adaptive control theory, the control for the hidden leader agent is designed by the desired reference signal, and the local control for each follower agent is designed using neighbourhood history information. Under the decentralised adaptive control, rigorous mathematical proofs are provided to show that the hidden leader agent tracks the desired reference signal, all the follower agents follow the hidden leader agent, and the closed-loop system eventually achieves strong synchronisation in the presence of strong couplings. In the end, the simulation results show the validity of this scheme.

Inspec keywords: decentralised control; closed loop systems; discrete time systems; autoregressive processes; adaptive control; multi-agent systems; nonlinear control systems

Other keywords: nonlinear discrete-time auto-regressive model; certainty equivalence principle; synchronisation; neighbourhood history information; projection algorithm; hidden leader-follower nonlinearly parameterised coupled MAS; decentralised adaptive control; closed-loop system

Subjects: Other topics in statistics; Discrete control systems; Self-adjusting control systems; Multivariable control systems; Nonlinear control systems

References

    1. 1)
      • 25. Ma, C.Q., Li, T., Zhang, J.F.: ‘Consensus control for leader-following multi-agent systems with measurement noises’, J. Syst. Sci. Complex., 2010, 23, pp. 3549.
    2. 2)
      • 22. Dong, W.J., Djapic, V.: ‘Leader-following control of multiple non-holonomic systems over directed communication graphs’, Int. J. Syst. Sci., 2016, 47, (8), pp. 18771890.
    3. 3)
      • 7. Liu, Q.Y., Wang, Z.D., He, X., et al.: ‘Event-based H consensus control of multi-agent systems with relative output feedback: the finite-horizon case’, IEEE Trans. Autom. Control, 2015, 60, (9), pp. 22532258.
    4. 4)
      • 32. Vamvoudakis, K.G., Lewis, F.L., Hudas, G.R.: ‘Multi-agent differential graphical games: online adaptive learning solution for synchronization with optimality’ (Pergamon Press, Inc., 2012).
    5. 5)
      • 11. Toshio, Y.: ‘Design of an adaptive fuzzy sliding mode control for uncertain discrete-time nonlinear systems based on noisy measurements’, Int. J. Syst. Sci., 2016, 47, pp. 617630.
    6. 6)
      • 34. Wang, W., Wen, C.Y., Huang, J.S.: ‘Distributed adaptive asymptotically consensus tracking control of nonlinear multi-agent systems with unknown parameters and uncertain disturbances’, Automatica, 2017, 77, pp. 133142.
    7. 7)
      • 21. Nourian, M., Caines, P.E., Malhamé, R.P., Huang, M.Y.: ‘Mean field LQG control in leader–follower stochastic multi-agent systems: likelihood ratio based adaptation’, IEEE Trans. Autom. Control, 2012, 57, (11), pp. 28012816.
    8. 8)
      • 35. Ge, S.S, Yang, C.G., Li, Y.N., et al: ‘Decentralized adaptive control of a class of discrete-time multi-agent systems for hidden leader following problem’. IEEE/RSJ Int. Conf. Intelligent Robots and Systems, 2009, pp. 50655070.
    9. 9)
      • 38. Ma, H.B.: ‘Decentralized adaptive synchronization of a stochastic discrete-time multi-agent dynamic model’, SIAM J. Control Optim., 2009, 48, (2), pp. 859880.
    10. 10)
      • 31. Ren, W.: ‘Multi-vehicle consensus with a time-varying reference state’, System & Control Letters, 2007, 56, (7-8), pp. 474483.
    11. 11)
      • 5. Ma, H.B., Lv, Y.N., Yang, C.G., et al.: ‘Decentralized adaptive filtering for multi-agent systems with uncertain couplings’, Acta Autom. Sin., 2014, 1, (1), pp. 94105.
    12. 12)
      • 23. Luo, X.Y., Han, N.N., Guan, X.P.: ‘Leader-following consensus protocols for formation control of multi-agent network’, Chin. J. Syst. Eng. Electron., 2011, 22, pp. 991997.
    13. 13)
      • 6. Liu, C.L., Liu, F.: ‘Delayed-compensation algorithm for second-order leader-following consensus seeking under communication delay’, Entropy, 2015, 17, (6), pp. 37523765.
    14. 14)
      • 12. Li, C.Y., Chen, M.Z.Q.: ‘Simultaneous identification and stabilization of nonlinearly parameterized discrete-time systems by nonlinear least squares algorithm’, IEEE Trans. Autom. Control, 2016, 61, (7), pp. 18101823.
    15. 15)
      • 39. Dong, G.H., He, H.G., Hu, D.W.: ‘A strict inequality on spectral radius of nonnegative matrices and its probabilistic proof’. Control Conf. 2008 CCC, 2008, pp. 138140.
    16. 16)
      • 3. Song, Q., Cao, J., Yu, W.W.: ‘Second-order leader-following consensus of nonlinear multi-agent systems via pinning control’, Syst. Control Lett., 2010, 59, pp. 553562.
    17. 17)
      • 16. Niu, Y.G., Lam, J., Wang, X.Y., et al.: ‘Neural adaptive sliding mode control for a class of nonlinear neutral delay systems’, J. Dyn. Syst. Meas. Control, 2008, 130, (6), pp. 758767.
    18. 18)
      • 13. Sokolov, V.F.: ‘Adaptive stabilization of parameter-affine minimum-phase plants under Lipschitz uncertainty’, Automatica, 2016, 73, pp. 6470.
    19. 19)
      • 1. Wang, X.K., Zeng, Z.W., Cong, Y.R.: ‘Multi-agent distributed coordination control: developments and directions via graph viewpoint’, Neurocomputing, 2016, 199, (26), pp. 204218.
    20. 20)
      • 28. Ren, W., Beard, R.W.: ‘Consensus seeking in multiagent systems under dynamically changing interaction topologies’, IEEE Trans. Autom. Control, 2005, 50, (5), pp. 655661.
    21. 21)
      • 29. Yu, H., Xia, X.H.: ‘Adaptive consensus of multi-agents in networks with jointly connected topologies’ (Pergamon Press, Inc., 2012).
    22. 22)
      • 14. Guo, L., Chen, H.F.: ‘The Aström–Wittenmark self-tuning regulator revisited and ELS-based adaptive trackers’, IEEE Trans. Autom. Control, 1991, 36, (7), pp. 802812.
    23. 23)
      • 4. Ni, W., Wang, X.L., Xiong, C.: ‘Consensus controllability, observability and robust design for leader-following linear multi-agent systems’, Automatica, 2013, 49, pp. 21992205.
    24. 24)
      • 27. Jadbabaie, A., Lin, J., Morse, A.S.: ‘Coordination of groups of mobile autonomous agents using nearest neighbor rules’, IEEE Trans. Autom. Control, 2003, 48, (9), pp. 16751675.
    25. 25)
      • 10. Li, C.Y., Lam, J.: ‘Stabilization of discrete-time nonlinear uncertain systems by feedback based on LS algorithm’, SIAMJ. Control Optim., 2013, 51, pp. 11281151.
    26. 26)
      • 9. Nadakuditi, R., Preisig, J.C.: ‘A channel subspace post-filtering approach to adaptive least-squares estimation’, IEEE Trans. Signal Process., 2002, 52, (7), pp. 19011914.
    27. 27)
      • 26. Wang, D., Huang, J.: ‘Adaptive neural network control for a class of uncertain nonlinear systems in pure-feedback form’, Automatica, 2002, 38, pp. 13651372.
    28. 28)
      • 33. Yu, H., Shen, Y.J., Xia, X.H.: ‘Adaptive finite-time consensus in multi-agent networks’, Syst. Control Lett., 2013, 62, (10), pp. 880889.
    29. 29)
      • 40. Guo, L.: ‘Time-varying stochastic systems–stability, estimation and control’ (Jilin Science and Technology Press, 1993).
    30. 30)
      • 15. Guo, L.: ‘Convergence and logarithm laws of self-tuning regulators’, Automatica, 1995, 31, pp. 435450.
    31. 31)
      • 18. Wen, C., Zhou, J.: ‘Decentralized adaptive stabilization in the presence of unknown backlash-like hysteresis’, Automatica, 2007, 43, (3), pp. 426440.
    32. 32)
      • 30. Das, A., Lewis, F.L.: ‘Distributed adaptive control for synchronization of unknown nonlinear networked systems’, Automatica, 2010, 46, (12), pp. 20142021.
    33. 33)
      • 20. Li, T., Zhang, J.F.: ‘Asymptotically optimal decentralized control for large population stochastic multiagent systems’, IEEE Trans. Autom. Control, 2008, 53, (7), pp. 16431659.
    34. 34)
      • 36. Yang, C.G., Li, Y., Ge, S.S., et al: ‘Adaptive control of a class of discrete-time MIMO nonlinear systems with uncertain couplings’, Int. J. Control, 2010, 83, (10), pp. 21202133.
    35. 35)
      • 37. Chen, L.J., Narendra, K.S.: ‘Nonlinear adaptive control using neural networks and multiple models’, Automatica, 2001, 37, pp. 12451255.
    36. 36)
      • 17. Liu, S.J., Zhang, J.F., Jiang, Z.P.: ‘Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems’, Automatica, 2007, 43, (2), pp. 238251.
    37. 37)
      • 2. Wang, C.Y., Ding, Z.T.: ‘H consensus control of multi-agent systems with input delay and directed topology’, Autom. Control Theory Appl., 2016, 10, (26), pp. 617624.
    38. 38)
      • 19. Belta, C., Kumar, V.: ‘Trajectory design for formations of robots by kinetic energy shaping’. IEEE Int. Conf. Robotics and Automation, 2002 Proc. ICRA, 2002, pp. 25932598.
    39. 39)
      • 24. Helbing, D., Farkas, I., Vicsek, T.: ‘Simulating dynamic features of escape panic’, Nature, 2000, 47, (6803), pp. 487490.
    40. 40)
      • 8. Yang, C.G., Ma, H.B., Fu, M.Y.: ‘Adaptive predictive control of periodic NARMA systems using nearest-neighbor compensation’, IET Control Theory Appl., 2013, 7, pp. 116.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2017.0644
Loading

Related content

content/journals/10.1049/iet-cta.2017.0644
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading