Advertisement

High-Order Discrete-Time Consensus

  • Yinyan Zhang
  • Shuai Li
Chapter
  • 28 Downloads

Abstract

In this chapter, we are concerned with the consensus of high-order discrete-time multi-agent systems. Normally, compared with low-order discrete-time multi-agent systems, the consensus of high-order ones would require the transmission of more information, leading to the increase of communication burden. In this chapter, present distributed discrete-time consensus protocols for such systems, for which the communication burden does not increase compared with the case of low-order ones. The consensus protocols allow different types of communication topologies, including static and time-varying ones. Both theoretical results about the performance of the protocols and the corresponding numerical examples are given.

References

  1. 1.
    M. Liu, X. Wang, Z. Li, Robust bipartite consensus and tracking control of high-order multiagent systems with matching uncertainties and antagonistic interactions. IEEE Trans. Syst. Man Cybern. Syst.  https://doi.org/10.1109/TSMC.2018.2821181
  2. 2.
    C. Zhao, X. Duan, Y. Shi, Analysis of consensus-based economic dispatch algorithm under time delays. IEEE Trans. Syst. Man Cybern. Syst..  https://doi.org/10.1109/TSMC.2018.2840821
  3. 3.
    T. Yang, D. Wu, Y. Sun, J. Lian, Minimum-time consensus-based approach for power system applications. IEEE Trans. Ind. Electron. 63(2), 1318–1328 (2016)CrossRefGoogle Scholar
  4. 4.
    Y. Zhang, S. Li, Predictive suboptimal consensus of multiagent systems with nonlinear dynamics. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1701–1711 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Z. Peng, G. Wen, S. Yang, A. Rahmani, Distributed consensus-based formation control for nonholonomic wheeled mobile robots using adaptive neural network. Nonlinear Dyn. 86(1), 605–622 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    S. Yang, Y. Cao, Z. Peng, G. Wen, K. Guo, Distributed formation control of nonholonomic autonomous vehicle via RBF neural network. Mech. Syst. Signal Process. 87, 81–95 (2017)CrossRefGoogle Scholar
  7. 7.
    L. Jin, S. Li, Distributed task allocation of multiple robots: a control perspective. IEEE Trans. Syst. Man Cybern. Syst. 48(5), 693–701 (2018)CrossRefGoogle Scholar
  8. 8.
    L. Jin, S. Li, H. M. La, X. Zhang, B. Hu, Dynamic task allocation in multi-robot coordination for moving target tracking: a distributed approach. Automatica 100, 75–81 (2019)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    L. Jin, S. Li, B. Hu, C. Yi, Dynamic neural networks aided distributed cooperative control of manipulators capable of different performance indices. Neurocomputing 291, 50–58 (2018)CrossRefGoogle Scholar
  10. 10.
    L. Jin, S. Li, L. Xiao, R. Lu, B. Liao, Cooperative motion generation in a distributed network of redundant robot manipulators with noises. IEEE Trans. Syst. Man Cybern. Syst. 48(10), 1715–1724 (2018)CrossRefGoogle Scholar
  11. 11.
    S. Li, M. Zhou, X. Luo, Z. You, Distributed winner-take-all in dynamic networks. IEEE Trans. Autom. Control 62(2), 577–589 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    S. Li, J. He, Y. Li, M.U. Rafique, Distributed recurrent neural networks for cooperative control of manipulators: a game-theoretic perspective. IEEE Trans. Neural Netw. Learn. Syst. 28(2), 415–426 (2017)MathSciNetCrossRefGoogle Scholar
  13. 13.
    L. Jin, S. Li, X. Luo, M. Shang, Nonlinearly-activated noise-tolerant zeroing neural network for distributed motion planning of multiple robot arms, in Proceedings of the International Joint Conference on Neural Networks (IJCNN) (IEEE, Piscataway, 2017), pp. 4165–4170Google Scholar
  14. 14.
    M.U. Khan, S. Li, Q. Wang, Z. Shao, Distributed multirobot formation and tracking control in cluttered environments. ACM Trans. Auton. Adapt. Syst. 11(2), 1–22 (2016)CrossRefGoogle Scholar
  15. 15.
    S. Li, Z. Wang, Y. Li, Using Laplacian eigenmap as heuristic information to solve nonlinear constraints defined on a graph and its application in distributed range-free localization of wireless sensor networks. Neural Process. Lett. 37(3), 411–424 (2013)CrossRefGoogle Scholar
  16. 16.
    L. Jin, S. Li, B. Hu, M. Liu, A survey on projection neural networks and their applications. Appl. Soft Comput. 76, 533–544 (2019)CrossRefGoogle Scholar
  17. 17.
    B. Liao, Q. Xiang, S. Li, Bounded Z-type neurodynamics with limited-time convergence and noise tolerance for calculating time-dependent Lyapunov equation. Neurocomputing 325, 234–241 (2019)CrossRefGoogle Scholar
  18. 18.
    P.S. Stanimirovic, V.N. Katsikis, S. Li, Integration enhanced and noise tolerant ZNN for computing various expressions involving outer inverses. Neurocomputing 329, 129–143 (2019)CrossRefGoogle Scholar
  19. 19.
    Z. Xu, S. Li, X. Zhou, W. Yan, T. Cheng, D. Huang, Dynamic neural networks based kinematic control for redundant manipulators with model uncertainties. Neurocomputing 329, 255–266 (2019)CrossRefGoogle Scholar
  20. 20.
    L. Xiao, K. Li, Z. Tan, Z. Zhang, B. Liao, K. Chen, L. Jin, S. Li, Nonlinear gradient neural network for solving system of linear equations. Inf. Process. Lett. 142, 35–40 (2019)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    D. Chen, S. Li, Q. Wu, Rejecting chaotic disturbances using a super-exponential-zeroing neurodynamic approach for synchronization of chaotic sensor systems. Sensors 19(1), 74 (2019)CrossRefGoogle Scholar
  22. 22.
    Q. Wu, X. Shen, Y. Jin, Z. Chen, S. Li, A.H. Khan, D. Chen, Intelligent beetle antennae search for UAV sensing and avoidance of obstacles. Sensors 19(8), 1758 (2019)CrossRefGoogle Scholar
  23. 23.
    Q. Xiang, B. Liao, L. Xiao, L. Lin, S. Li, Discrete-time noise-tolerant Zhang neural network for dynamic matrix pseudoinversion. Soft Comput. 23(3), 755–766 (2019)zbMATHCrossRefGoogle Scholar
  24. 24.
    Z. Zhang, S. Chen, S. Li, Compatible convex-nonconvex constrained QP-based dual neural networks for motion planning of redundant robot manipulators. IEEE Trans. Contr. Syst. Technol. 27(3), 1250–1258 (2019)CrossRefGoogle Scholar
  25. 25.
    Y. Zhang, S. Li, X. Zhou, Recurrent-neural-network-based velocity-level redundancy resolution for manipulators subject to a joint acceleration limit. IEEE Trans. Ind. Electron. 66(5), 3573–3582 (2019)CrossRefGoogle Scholar
  26. 26.
    L. Jin, S. Li, B. Hu, M. Liu, J. Yu, A noise-suppressing neural algorithm for solving the time-varying system of linear equations: a control-based approach. IEEE Trans. Ind. Inf. 15(1), 236–246 (2019)CrossRefGoogle Scholar
  27. 27.
    Y. Li, S. Li, B. Hannaford, A model-based recurrent neural network with randomness for efficient control with applications. IEEE Trans. Ind. Inf. 15(4), 2054–2063 (2019)CrossRefGoogle Scholar
  28. 28.
    L. Xiao, S. Li, F. Lin, Z. Tan, A. H. Khan, Zeroing neural dynamics for control design: Comprehensive analysis on stability, robustness, and convergence speed. IEEE Trans. Ind. Inf. 15(5), 2605–2616 (2019)CrossRefGoogle Scholar
  29. 29.
    S. Muhammad, M.U. Rafique, S. Li, Z. Shao, Q. Wang, X. Liu, Reconfigurable battery systems: a survey on hardware architecture and research challenges. ACM Trans. Des. Autom. Electron. Syst. 24(2), 19:1–19:27 (2019)CrossRefGoogle Scholar
  30. 30.
    S. Li, Z. Shao, Y. Guan, A dynamic neural network approach for efficient control of manipulators. IEEE Trans. Syst. Man Cybern. Syst. 49(5), 932–941 (2019)CrossRefGoogle Scholar
  31. 31.
    L. Jin, S. Li, H. Wang, Z. Zhang, Nonconvex projection activated zeroing neurodynamic models for time-varying matrix pseudoinversion with accelerated finite-time convergence. Appl. Soft Comput. 62, 840–850 (2018)CrossRefGoogle Scholar
  32. 32.
    M. Liu, S. Li, X. Li, L. Jin, C. Yi, Z. Huang, Intelligent controllers for multirobot competitive and dynamic tracking. Complexity 2018, 4573631:1–4573631:12 (2018)zbMATHGoogle Scholar
  33. 33.
    D. Chen, Y. Zhang, S. Li, Zeroing neural-dynamics approach and its robust and rapid solution for parallel robot manipulators against superposition of multiple disturbances. Neurocomputing 275, 845–858 (2018)CrossRefGoogle Scholar
  34. 34.
    L. Jin, S. Li, J. Yu, J. He, Robot manipulator control using neural networks: a survey. Neurocomputing 285, 23–34 (2018)CrossRefGoogle Scholar
  35. 35.
    L. Xiao, S. Li, J. Yang, Z. Zhang, A new recurrent neural network with noise-tolerance and finite-time convergence for dynamic quadratic minimization. Neurocomputing 285, 125–132 (2018)CrossRefGoogle Scholar
  36. 36.
    P.S. Stanimirovic, V.N. Katsikis, S. Li, Hybrid GNN-ZNN models for solving linear matrix equations. Neurocomputing 316, 124–134 (2018)CrossRefGoogle Scholar
  37. 37.
    X. Li, J. Yu, S. Li, L. Ni, A nonlinear and noise-tolerant ZNN model solving for time-varying linear matrix equation. Neurocomputing 317, 70–78 (2018)CrossRefGoogle Scholar
  38. 38.
    L. Xiao, B. Liao, S. Li, K. Chen, Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations. Neural Netw. 98, 102–113 (2018)CrossRefGoogle Scholar
  39. 39.
    L. Xiao, Z. Zhang, Z. Zhang, W. Li, S. Li, Design, verification and robotic application of a novel recurrent neural network for computing dynamic Sylvester equation. Neural Netw. 105, 185–196 (2018)CrossRefGoogle Scholar
  40. 40.
    Z. Zhang, Y. Lu, L. Zheng, S. Li, Z. Yu, Y. Li, A new varying-parameter convergent-differential neural-network for solving time-varying convex QP problem constrained by linear-equality. IEEE Trans. Autom. Control 63(12), 4110–4125 (2018)MathSciNetzbMATHCrossRefGoogle Scholar
  41. 41.
    Z. Zhang, Y. Lin, S. Li, Y. Li, Z. Yu, Y. Luo, Tricriteria optimization-coordination motion of dual-redundant-robot manipulators for complex path planning. IEEE Trans. Control Syst. Technol. 26(4), 1345–1357 (2018)CrossRefGoogle Scholar
  42. 42.
    X. Luo, M. Zhou, S. Li, Y. Xia, Z. You, Q. Zhu, H. Leung, Incorporation of efficient second-order solvers into latent factor models for accurate prediction of missing QoS data. IEEE Trans. Cybern. 48(4), 1216–1228 (2018)CrossRefGoogle Scholar
  43. 43.
    L. Xiao, B. Liao, S. Li, Z. Zhang, L. Ding, L. Jin, Design and analysis of FTZNN applied to the real-time solution of a nonstationary Lyapunov equation and tracking control of a wheeled mobile manipulator. IEEE Trans. Ind. Inf. 14(1), 98–105 (2018)CrossRefGoogle Scholar
  44. 44.
    L. Jin, S. Li, B. Hu, RNN models for dynamic matrix inversion: a control-theoretical perspective. IEEE Trans. Ind. Inf. 14(1), 189–199 (2018)CrossRefGoogle Scholar
  45. 45.
    X. Luo, M. Zhou, S. Li, M. Shang, An inherently nonnegative latent factor model for high-dimensional and sparse matrices from industrial applications. IEEE Trans. Ind. Inf. 14(5), 2011–2022 (2018)CrossRefGoogle Scholar
  46. 46.
    D. Chen, Y. Zhang, S. Li, Tracking control of robot manipulators with unknown models: a Jacobian-matrix-adaption method. IEEE Trans. Ind. Inf. 14(7), 3044–3053 (2018)CrossRefGoogle Scholar
  47. 47.
    J. Li, Y. Zhang, S. Li, M. Mao, New discretization-formula-based zeroing dynamics for real-time tracking control of serial and parallel manipulators. IEEE Trans. Ind. Inf. 14(8), 3416–3425 (2018)CrossRefGoogle Scholar
  48. 48.
    S. Li, H. Wang, M.U. Rafique, A novel recurrent neural network for manipulator control with improved noise tolerance. IEEE Trans. Neural Netw. Learn. Syst. 29(5), 1908–1918 (2018)MathSciNetCrossRefGoogle Scholar
  49. 49.
    H. Wang, P.X. Liu, S. Li, D. Wang, Adaptive neural output-feedback control for a class of nonlower triangular nonlinear systems with unmodeled dynamics. IEEE Trans. Neural Netw. Learn. Syst. 29(8), 3658–3668 (2018)MathSciNetCrossRefGoogle Scholar
  50. 50.
    S. Li, M. Zhou, X. Luo, Modified primal-dual neural networks for motion control of redundant manipulators with dynamic rejection of harmonic noises. IEEE Trans. Neural Netw. Learn. Syst. 29(10), 4791–4801 (2018)MathSciNetCrossRefGoogle Scholar
  51. 51.
    Y. Li, S. Li, B. Hannaford, A novel recurrent neural network for improving redundant manipulator motion planning completeness, in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) (IEEE, Piscataway, 2018), pp. 2956–2961Google Scholar
  52. 52.
    M.A. Mirza, S. Li, L. Jin, Simultaneous learning and control of parallel Stewart platforms with unknown parameters. Neurocomputing 266, 114–122 (2017)CrossRefGoogle Scholar
  53. 53.
    L. Jin, S. Li, Nonconvex function activated zeroing neural network models for dynamic quadratic programming subject to equality and inequality constraints. Neurocomputing 267, 107–113 (2017)CrossRefGoogle Scholar
  54. 54.
    L. Jin, S. Li, B. Liao, Z. Zhang, Zeroing neural networks: a survey. Neurocomputing 267, 597–604 (2017)CrossRefGoogle Scholar
  55. 55.
    L. Jin, Y. Zhang, S. Li, Y. Zhang, Noise-tolerant ZNN models for solving time-varying zero-finding problems: a control-theoretic approach. IEEE Trans. Autom. Control 62(2), 992–997 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  56. 56.
    Z. You, M. Zhou, X. Luo, S. Li, Highly efficient framework for predicting interactions between proteins. IEEE Trans. Cybern. 47(3), 731–743 (2017)CrossRefGoogle Scholar
  57. 57.
    L. Jin, S. Li, H. M. La, X. Luo, Manipulability optimization of redundant manipulators using dynamic neural networks. IEEE Trans. Ind. Electron. 64(6), 4710–4720 (2017)CrossRefGoogle Scholar
  58. 58.
    S. Muhammad, M.U. Rafique, S. Li, Z. Shao, Q. Wang, N. Guan, A robust algorithm for state-of-charge estimation with gain optimization. IEEE Trans. Ind. Inf. 13(6), 2983–2994 (2017)CrossRefGoogle Scholar
  59. 59.
    X. Luo, J. Sun, Z. Wang, S. Li, M. Shang, Symmetric and nonnegative latent factor models for undirected, high-dimensional, and sparse networks in industrial applications. IEEE Trans. Ind. Inf. 13(6), 3098–3107 (2017)CrossRefGoogle Scholar
  60. 60.
    S. Li, Y. Zhang, L. Jin, Kinematic control of redundant manipulators using neural networks. IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2243–2254 (2017)MathSciNetCrossRefGoogle Scholar
  61. 61.
    X. Luo, S. Li, Non-negativity constrained missing data estimation for high-dimensional and sparse matrices, in Proceedings of the 13th IEEE Conference on Automation Science and Engineering (CASE) (IEEE, Piscataway, 2017), pp. 1368–1373Google Scholar
  62. 62.
    Y. Li, S. Li, D.E. Caballero, M. Miyasaka, A. Lewis, B. Hannaford, Improving control precision and motion adaptiveness for surgical robot with recurrent neural network, in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE, Piscataway, 2017), pp. 3538–3543Google Scholar
  63. 63.
    X. Luo, M. Zhou, M. Shang, S. Li, Y. Xia, A novel approach to extracting non-negative latent factors from non-negative big sparse matrices. IEEE Access 4, 2649–2655 (2016)CrossRefGoogle Scholar
  64. 64.
    M. Mao, J. Li, L. Jin, S. Li, Y. Zhang, Enhanced discrete-time Zhang neural network for time-variant matrix inversion in the presence of bias noises. Neurocomputing 207, 220–230 (2016)CrossRefGoogle Scholar
  65. 65.
    Y. Huang, Z. You, X. Li, X. Chen, P. Hu, S. Li, X. Luo, Construction of reliable protein-protein interaction networks using weighted sparse representation based classifier with pseudo substitution matrix representation features. Neurocomputing 218, 131–138 (2016)CrossRefGoogle Scholar
  66. 66.
    X. Luo, M. Zhou, H. Leung, Y. Xia, Q. Zhu, Z. You, S. Li, An incremental-and-static-combined scheme for matrix-factorization-based collaborative filtering. IEEE Trans. Autom. Sci. Eng. 13(1), 333–343 (2016)CrossRefGoogle Scholar
  67. 67.
    S. Li, Z. You, H. Guo, X. Luo, Z. Zhao, Inverse-free extreme learning machine with optimal information updating. IEEE Trans. Cybern. 46(5), 1229–1241 (2016)CrossRefGoogle Scholar
  68. 68.
    L. Jin, Y. Zhang, S. Li, Y. Zhang, Modified ZNN for time-varying quadratic programming with inherent tolerance to noises and its application to kinematic redundancy resolution of robot manipulators. IEEE Trans. Ind. Electron. 63(11), 6978–6988 (2016)CrossRefGoogle Scholar
  69. 69.
    X. Luo, M. Zhou, S. Li, Z. You, Y. Xia, Q. Zhu, A nonnegative latent factor model for large-scale sparse matrices in recommender systems via alternating direction method. IEEE Trans. Neural Netw. Learn. Syst. 27(3), 579–592 (2016)MathSciNetCrossRefGoogle Scholar
  70. 70.
    L. Jin, Y. Zhang, S. Li, Integration-enhanced Zhang neural network for real-time-varying matrix inversion in the presence of various kinds of noises. IEEE Trans. Neural Netw. Learn. Syst. 27(12), 2615–2627 (2016)CrossRefGoogle Scholar
  71. 71.
    X. Luo, M. Shang, S. Li, Efficient extraction of non-negative latent factors from high-dimensional and sparse matrices in industrial applications, in Proceedings of the IEEE 16th International Conference on Data Mining (ICDM) (IEEE, Piscataway, 2016), pp. 311–319Google Scholar
  72. 72.
    X. Luo, S. Li, M. Zhou, Regularized extraction of non-negative latent factors from high-dimensional sparse matrices, in Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics (SMC) (IEEE, Piscataway, 2016), pp. 1221–1226Google Scholar
  73. 73.
    X. Luo, Z. Ming, Z. You, S. Li, Y. Xia, H. Leung, Improving network topology-based protein interactome mapping via collaborative filtering. Knowl.-Based Syst. 90, 23–32 (2015)CrossRefGoogle Scholar
  74. 74.
    X. Luo, M. Zhou, S. Li, Y. Xia, Z. You, Q. Zhu, H. Leung, An efficient second-order approach to factorize sparse matrices in recommender systems. IEEE Trans. Ind. Inf. 11(4), 946–956 (2015)CrossRefGoogle Scholar
  75. 75.
    L. Wong, Z. You, S. Li, Y. Huang, G. Liu, Detection of protein-protein interactions from amino acid sequences using a rotation forest model with a novel PR-LPQ descriptor, in Proceedings of the International Conference on Intelligent Computing ICIC (Springer, Cham, 2015), pp. 713–720Google Scholar
  76. 76.
    Z. You, J. Yu, L. Zhu, S. Li, Z. Wen, A MapReduce based parallel SVM for large-scale predicting protein-protein interactions. Neurocomputing 145, 37–43 (2014)CrossRefGoogle Scholar
  77. 77.
    Y. Li, S. Li, Q. Song, H. Liu, M.Q.H. Meng, Fast and robust data association using posterior based approximate joint compatibility test. IEEE Trans. Ind. Inf. 10(1), 331–339 (2014)CrossRefGoogle Scholar
  78. 78.
    S. Li, Y. Li, Nonlinearly activated neural network for solving time-varying complex Sylvester equation. IEEE Trans. Cybern. 44(8), 1397–1407 (2014)CrossRefGoogle Scholar
  79. 79.
    Q. Huang, Z. You, S. Li, Z. Zhu, Using Chou’s amphiphilic pseudo-amino acid composition and extreme learning machine for prediction of protein-protein interactions, in Proceedings of the International Joint Conference on Neural Networks (IJCNN) (IEEE, Piscataway, 2014), pp. 2952–2956Google Scholar
  80. 80.
    S. Li, Y. Li, Z. Wang, A class of finite-time dual neural networks for solving quadratic programming problems and its k-winners-take-all application. Neural Netw. 39, 27–39 (2013)zbMATHCrossRefGoogle Scholar
  81. 81.
    S. Li, B. Liu, Y. Li, Selective positive-negative feedback produces the winner-take-all competition in recurrent neural networks. IEEE Trans. Neural Netw. Learn. Syst. (24)(2), 301–309 (2013)Google Scholar
  82. 82.
    Y. Cao, W. Ren, Sampled-data discrete-time coordination algorithms for double-integrator dynamics under dynamic directed interaction. Int. J. Control 83(3), 506–515 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  83. 83.
    Y. Liu, S. Li, S. Tong, C.L.P. Chen, Neural approximation-based adaptive control for a class of nonlinear nonstrict feedback discrete-time systems. IEEE Trans. Neural Netw. Learn. Syst. 28(7), 1531–1541 (2017)MathSciNetCrossRefGoogle Scholar
  84. 84.
    Y. Liu, S. Tong, Optimal control-based adaptive NN design for a class of nonlinear discrete-time block-triangular systems. IEEE Trans. Cybern. 46(11), 2670–2680 (2016)CrossRefGoogle Scholar
  85. 85.
    X. Xie, Q. Zhou, D. Yue, H. Li, Relaxed control design of discrete-time Takagi-Sugeno fuzzy systems: an event-triggered real-time scheduling approach. IEEE Trans. Syst. Man Cybern. Syst..  https://doi.org/10.1109/TSMC.2017.2737542 CrossRefGoogle Scholar
  86. 86.
    Y. Liu, Y. Gao, S. Tong, C.L.P. Chen, A unified approach to adaptive neural control for nonlinear discrete-time systems with nonlinear dead-zone input. IEEE Trans. Neural Netw. Learn. Syst. 27(1), 139–150 (2016)MathSciNetCrossRefGoogle Scholar
  87. 87.
    Y. Liu, L. Tang, S. Tong, C.L.P. Chen, D. Li, Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discrete-time MIMO systems. IEEE Trans. Neural Netw. Learn. Syst. 26(1), 165–176 (2015)MathSciNetCrossRefGoogle Scholar
  88. 88.
    R. Olfati-Saber, R.M. Murry, Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  89. 89.
    Y. Zhang, S. Li, Predictive suboptimal consensus of multiagent systems with nonlinear dynamics. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1701–1711 (2017)MathSciNetCrossRefGoogle Scholar
  90. 90.
    C.L.P. Chen, G.X. Wen, Y.J. Liu, Z. Liu, Observer-based adaptive backstepping consensus tracking control for high-order nonlinear semi-strict-feedback multiagent systems. IEEE Trans. Cybern. 46(7), 1591–1601 (2016)CrossRefGoogle Scholar
  91. 91.
    W. Zhang, Y. Tang, T. Huang, A.V. Vasilakos, Consensus of networked Euler-Lagrange systems under time-varying sampled-data control. IEEE Trans. Ind. Inf. 14(2), 535–544 (2018)CrossRefGoogle Scholar
  92. 92.
    Y. Zhang, S. Li, Adaptive near-optimal consensus of high-order nonlinear multi-agent systems with heterogeneity. Automatica 85, 426–432 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  93. 93.
    L. Moreau, Stability of multiagent systems with time-dependent communication links. IEEE Trans. Autom. Control 50(2), 169–181 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  94. 94.
    Y. Su, J. Huang, Two consensus problems for discrete-time multi-agent systems with switching network topology. Automatica 48(9), 1988–1997 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  95. 95.
    Y. Wei, G.P. Liu, Consensus tracking of heterogeneous discrete-time networked multiagent systems based on the networked predictive control scheme. IEEE Trans. Cybern. 47(8), 2173–2184 (2017)CrossRefGoogle Scholar
  96. 96.
    P. Lin, Y. Jia, Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies. Automatica 45(9), 2154–2158 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  97. 97.
    J. Qin, C. Yu, S. Hirche, Stationary consensus of asynchronous discrete-time second-order multi-agent systems under switching topology. IEEE Trans. Ind. Inf. 8(4), 986–994 (2012)CrossRefGoogle Scholar
  98. 98.
    S.M. Dibaji, H. Ishii, Resilient consensus of second-order agent networks: asynchronous update rules with delays. Automatica 81, 123–132 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  99. 99.
    D. Xie, S. Wang, Consensus of second-order discrete-time multi-agent systems with fixed topology. J. Math. Anal. Appl. (387)(1), 8–16 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  100. 100.
    Y. Chen, J. Lü, X. Yu, Z. Lin, Consensus of discrete-time second-order multiagent systems based on infinite products of general stochastic matrices. SIAM J. Control Optim. 51(4), 3274–3301 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  101. 101.
    J. Zhu, Y.P. Tian, J. Kuang, On the general consensus protocol of multi-agent systems with double-integrator dynamics. Linear Algebra Appl. 431(5), 701–715 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  102. 102.
    F. Sun, Z.H. Guan, X.S. Zhan, F.S. Yuan, Consensus of second-order and high-order discrete-time multi-agent systems with random networks. Nonlinear Anal. Real World Appl. 13(5), 1979–1990 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  103. 103.
    W. He, J. Cao, Consensus control for high-order multi-agent systems. IET Control Theory Appl. 5(1), 231–238 (2011)MathSciNetCrossRefGoogle Scholar
  104. 104.
    L. Macellari, Y. Karayiannidis, D.V. Dimarogonas, Multi-agent second order average consensus with prescribed transient behavior. IEEE Trans. Autom. Control 62(10), 5282–5288 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  105. 105.
    Y. Zhang, S. Li, Perturbing consensus for complexity: a finite-time discrete biased min-consensus under time-delay and asynchronism. Automatica 85, 441–447 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  106. 106.
    J. Cortés, Distributed algorithms for reaching consensus on general functions. Automatica 44(3), 726–737 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  107. 107.
    T. Li, M. Fu, L. Xie, J.F. Zhang, Distributed consensus with limited communication data rate. IEEE Trans. Autom. Control 56(2), 279–292 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  108. 108.
    K. You, L. Xie, Network topology and communication data rate for consensusability of discrete-time multi-agent systems. IEEE Trans. Autom. Control 56(10), 2262–2275 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  109. 109.
    K.S. Narendra, C. Xiang, Adaptive control of discrete-time systems using multiple models. IEEE Trans. Autom. Control 45(9), 1669–1686 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  110. 110.
    E.A. Khidir, N.A. Mohamed, M.J.M. Nor, M.M. Mustafa, A new concept of a linear smart actuator. Sensors Actuators A 135(1), 244–249 (2007)CrossRefGoogle Scholar
  111. 111.
    H. Wu, D. Sun, Z. Zhou, Model identification of a micro air vehicle in loitering flight based on attitude performance evaluation. IEEE Trans. Robot. 20(4), 702–712 (2004)CrossRefGoogle Scholar
  112. 112.
    I.D. Landau, G. Zito, Digital Control Systems: Design, Identification And Implementation (Springer, New York, 2006)Google Scholar
  113. 113.
    S. Knorn, Z. Chen, R.H. Middleton, Overview: collective control of multiagent systems. IEEE Trans. Control Netw. Syst. 3(4), 334–347 (2016)MathSciNetzbMATHCrossRefGoogle Scholar
  114. 114.
    H. Yu, X. Xia, Adaptive consensus of multi-agents in networks with jointly connected topologies. Automatica 48(8), 1783–1790 (2012)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Yinyan Zhang
    • 1
  • Shuai Li
    • 2
  1. 1.College of Cyber SecurityJinan UniversityGuangzhouChina
  2. 2.School of EngineeringSwansea UniversitySwanseaUK

Personalised recommendations