Discrete-Time Biased Min-Consensus

  • Yinyan Zhang
  • Shuai Li


In this chapter, we discuss a modified discrete-time min-consensus protocol by adding a biased term, which is referred to as the discrete-time biased min-consensus protocol and is convergent in finite time. It should be noted that the protocol here is not obtained by using difference rules to the continuous-time biased min-consensus protocol in the previous chapter, and thus the theoretical analysis is different. The convergence property of the discrete-time biased min-consensus protocol is also analyzed in the case with time delay and asynchronous updating of state variables. We also find that a complex behavior, i.e., finding a shortest path over a graph, can emerge from such a modified protocol. The protocol is also evaluated by different simulation scenarios.


  1. 1.
    J. Cortés, Distributed algorithms for reaching consensus on general functions. Automatica 44(3), 726–737 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    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
  3. 3.
    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
  4. 4.
    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
  5. 5.
    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
  6. 6.
    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
  7. 7.
    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
  8. 8.
    L. Jin, S. Li, X. Luo, M. Shang, Nonlinearly-activated noise-tolerant zeroing neural network for distributed motion planning of multiple robot arms, in Proceeding of 2014 International Joint Conference on Neural Networks (IJCNN) (2017), pp. 4165–4170Google Scholar
  9. 9.
    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
  10. 10.
    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
  11. 11.
    S. Li, Y. Guo, Distributed consensus filter on directed switching graphs. Int. J. Robust Nonlinear Control 25(13), 2019–2040 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    N. Abaid, M. Porfiri, Leader-follower consensus over numerosity-constrained random networks. Automatica 48(8), 1845–1851 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    R. Olfati-Saber, R.M. Murray, Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)MathSciNetzbMATHGoogle Scholar
  14. 14.
    K. Cai, H. Ishii, Average consensus on general strongly connected digraphs. Automatica 48(11), 2750–2761 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    F. Xiao, L. Wang, Consensus protocols for discrete-time multi-agent systems with time-varying delays. Automatica 44(10), 2577–2582 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    X. Xu, S. Chen, W. Huang, L. Gao, Leader-following consensus of discrete-time multi-agent systems with observer-based protocols. Neurocomputing 118(22), 334–341 (2013)CrossRefGoogle Scholar
  17. 17.
    Y. Chen, J. Lü, Z. Lin, Consensus of discrete-time multi-agent systems with transmission nonlinearity. Automatica 49(6), 1768–1775 (2013)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    T. Yang, Z. Meng, D.V. Dimarogonas, K.H. Johansson, Global consensus for discrete-time multi-agent systems with input saturation constraints. Automatica 50(2), 499–506 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    J. He, L. Duan, F. Hou, P. Cheng, J. Chen, Multiperiod scheduling for wireless sensor networks: a distributed consensus approach. IEEE Trans. Signal Process. 63(7), 1651–1663 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    S.T. Cady, A.D. Domíguez-García, C.N. Hadjicostis, Finite-time approximate consensus and its application to distributed frequency regulation in islanded AC microgrids, in Proceeding of 48th Hawaii International Conference of System Science (2015), pp. 2664–2670Google Scholar
  21. 21.
    V. Yadav, M.V. Salapaka, Distributed protocol for determining when averaging consensus is reached, in Proceeding of 45th Annual Allerton Conference Communication, Control, Computer (2007), pp. 715–720Google Scholar
  22. 22.
    L. Fu, D. Sun, L.R. Rilett, Heuristic shortest path algorithms for transportation applications: state of the art. Comput. Oper. Res. 33, 3324–3343 (2006)zbMATHCrossRefGoogle Scholar
  23. 23.
    E.W. Dijkstra, A note on two problems in connexion with graphs. Numer. Math. 1(1), 269–271 (1959)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    C.W. Ahn, R.S. Ramakrishna, A genetic algorithm for shortest path routing problem and the sizing of populations. IEEE Trans. Evol. Comput. 6(6), 566–579 (2002)CrossRefGoogle Scholar
  25. 25.
    A.W. Mohemmed, N.C. Sahoo, T.K. Geok, Solving shortest path problem using particle swarm optimization. Appl. Soft Comput. 8(4), 1643–653 (2008)CrossRefGoogle Scholar
  26. 26.
    G.E. Jan, C. Sun, W.C. Tsai, T. Lin, An O(nlogn) shortest path algorithm based on Delaunay triangulation. IEEE/ASME Trans. Mechatron. 19(2), 660–666 (2014)CrossRefGoogle Scholar
  27. 27.
    Y. Sang, J. Lv, H. Qu, Z. Yi, Shortest path computation using pulse-coupled neural networks with restricted autowave. Know. Syst. 114, 1–11 (2016)CrossRefGoogle Scholar
  28. 28.
    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
  29. 29.
    Z. Ni, H. He, J. Wen, X. Xu, Goal representation heuristic dynamic programming on maze navigation. IEEE Trans. Neural Netw. Learn. Syst. 24(12), 2038–2050 (2013)CrossRefGoogle Scholar
  30. 30.
    S.X. Yang, C. Luo, A neural network approach to complete coverage path planning. IEEE Trans. Syst. Man Cybern. Part B Cybern. 34(1), 718–725 (2004)CrossRefGoogle Scholar
  31. 31.
    L. Wang, F. Xiao, Finite-time consensus problems for networks of dynamic agents. IEEE Trans. Autom. Control 55(4), 950–955 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    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
  33. 33.
    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
  34. 34.
    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
  35. 35.
    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
  36. 36.
    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
  37. 37.
    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
  38. 38.
    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
  39. 39.
    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
  40. 40.
    Z. Zhang, S. Chen, S. Li, Compatible convex-nonconvex constrained QP-based dual neural networks for motion planning of redundant robot manipulators. IEEE Trans. Control Syst. Technol. 27(3), 1250–1258 (2019)CrossRefGoogle Scholar
  41. 41.
    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
  42. 42.
    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
  43. 43.
    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
  44. 44.
    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
  45. 45.
    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
  46. 46.
    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
  47. 47.
    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
  48. 48.
    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
  49. 49.
    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
  50. 50.
    L. Jin, S. Li, J. Yu, J. He, Robot manipulator control using neural networks: a survey. Neurocomputing 285, 23–34 (2018)CrossRefGoogle Scholar
  51. 51.
    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
  52. 52.
    P.S. Stanimirovic, V.N. Katsikis, S. Li, Hybrid GNN-ZNN models for solving linear matrix equations. Neurocomputing 316, 124–134 (2018)CrossRefGoogle Scholar
  53. 53.
    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
  54. 54.
    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
  55. 55.
    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
  56. 56.
    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
  57. 57.
    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
  58. 58.
    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
  59. 59.
    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
  60. 60.
    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
  61. 61.
    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
  62. 62.
    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
  63. 63.
    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
  64. 64.
    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
  65. 65.
    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
  66. 66.
    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
  67. 67.
    Y. Li, S. Li, B. Hannaford, A novel recurrent neural network for improving redundant manipulator motion planning completeness, in Proceeding of 2018 IEEE International Conference on Robotics and Automation (ICRA) (2018), pp. 2956–2961Google Scholar
  68. 68.
    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
  69. 69.
    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
  70. 70.
    L. Jin, S. Li, B. Liao, Z. Zhang, Zeroing neural networks: a survey. Neurocomputing 267, 597–604 (2017)CrossRefGoogle Scholar
  71. 71.
    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
  72. 72.
    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
  73. 73.
    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
  74. 74.
    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
  75. 75.
    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
  76. 76.
    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
  77. 77.
    X. Luo, S. Li, Non-negativity constrained missing data estimation for high-dimensional and sparse matrices, in Proceeding of 2017 13th IEEE Conference on Automation Science and Engineering (CASE) (2017), pp. 1368–1373Google Scholar
  78. 78.
    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 Proceeding of 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (2017), pp. 3538–3543Google Scholar
  79. 79.
    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
  80. 80.
    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
  81. 81.
    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
  82. 82.
    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
  83. 83.
    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
  84. 84.
    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
  85. 85.
    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
  86. 86.
    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
  87. 87.
    X. Luo, M. Shang, S. Li, Efficient extraction of non-negative latent factors from high-dimensional and sparse matrices in industrial applications, in Proceeding of 2016 IEEE 16th International Conference on Data Mining (ICDM) (2016), pp. 311–319Google Scholar
  88. 88.
    X. Luo, S. Li, M. Zhou, Regularized extraction of non-negative latent factors from high-dimensional sparse matrices, in Proceeding of 2016 IEEE International Conference on Systems, Man, and Cybernetics (SMC) (2016), pp. 1221–1226Google Scholar
  89. 89.
    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
  90. 90.
    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
  91. 91.
    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 Proceeding of International Conference on Intelligent Computing, vol. 2015 (2015), pp. 713–720Google Scholar
  92. 92.
    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
  93. 93.
    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
  94. 94.
    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
  95. 95.
    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 Proceeding of 2014 International Joint Conference on Neural Networks (IJCNN) (2014), pp. 2952–2956Google Scholar
  96. 96.
    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
  97. 97.
    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)MathSciNetCrossRefGoogle Scholar
  98. 98.
    S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge University Press, Cambridge, 2004)zbMATHCrossRefGoogle Scholar
  99. 99.
    S. Fang, H. Chan, Human identification by quantifying similarity and dissimilarity in electrocardiogram phase space. Pattern Recog. 42, 1824–1831 (2009)CrossRefGoogle Scholar
  100. 100.
    L. Fang, P.J. Antsaklis, Information consensus of asynchronous discrete-time multi-agent systems, in Proceeding of 2005 American Control Conference (2005), pp. 1883–1888Google Scholar
  101. 101.
    E. Galceran, M. Carreras, A survey on coverage path planning for robotics. Robot. Auton. Syst. 61(12), 1258–1276 (2013)CrossRefGoogle Scholar
  102. 102.
    C.H. Kuo, H.C. Chou, S.Y. Tasi, Pneumatic sensor: a complete coverage improvement approach for robotic cleaners. IEEE Trans. Instrum. Meas. 60(4), 1237–1256 (2011)CrossRefGoogle Scholar
  103. 103.
    O. Slućiak, M. Rupp, Network size estimation using distributed orthogonalization. IEEE Signal Process. Lett. 20(4), 347–350 (2013)CrossRefGoogle 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

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