Machine Behavior Design And Analysis pp 73-96 | Cite as

# Discrete-Time Biased Min-Consensus

- 34 Downloads

## Abstract

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.

## References

- 1.J. Cortés, Distributed algorithms for reaching consensus on general functions. Automatica
**44**(3), 726–737 (2008)MathSciNetzbMATHCrossRefGoogle Scholar - 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.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.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.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.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.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.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.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.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.S. Li, Y. Guo, Distributed consensus filter on directed switching graphs. Int. J. Robust Nonlinear Control
**25**(13), 2019–2040 (2015)MathSciNetzbMATHCrossRefGoogle Scholar - 12.N. Abaid, M. Porfiri, Leader-follower consensus over numerosity-constrained random networks. Automatica
**48**(8), 1845–1851 (2012)MathSciNetzbMATHCrossRefGoogle Scholar - 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.K. Cai, H. Ishii, Average consensus on general strongly connected digraphs. Automatica
**48**(11), 2750–2761 (2012)MathSciNetzbMATHCrossRefGoogle Scholar - 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.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.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.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.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.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.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.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.E.W. Dijkstra, A note on two problems in connexion with graphs. Numer. Math.
**1**(1), 269–271 (1959)MathSciNetzbMATHCrossRefGoogle Scholar - 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.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.G.E. Jan, C. Sun, W.C. Tsai, T. Lin, An
*O*(*n*log*n*) shortest path algorithm based on Delaunay triangulation. IEEE/ASME Trans. Mechatron.**19**(2), 660–666 (2014)CrossRefGoogle Scholar - 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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.L. Jin, S. Li, J. Yu, J. He, Robot manipulator control using neural networks: a survey. Neurocomputing
**285**, 23–34 (2018)CrossRefGoogle Scholar - 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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.L. Jin, S. Li, B. Liao, Z. Zhang, Zeroing neural networks: a survey. Neurocomputing
**267**, 597–604 (2017)CrossRefGoogle Scholar - 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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.S. Boyd, L. Vandenberghe,
*Convex Optimization*(Cambridge University Press, Cambridge, 2004)zbMATHCrossRefGoogle Scholar - 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.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.E. Galceran, M. Carreras, A survey on coverage path planning for robotics. Robot. Auton. Syst.
**61**(12), 1258–1276 (2013)CrossRefGoogle Scholar - 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.O. Slućiak, M. Rupp, Network size estimation using distributed orthogonalization. IEEE Signal Process. Lett.
**20**(4), 347–350 (2013)CrossRefGoogle Scholar