A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 7 Issue 6
Oct.  2020

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 15.3, Top 1 (SCI Q1)
    CiteScore: 23.5, Top 2% (Q1)
    Google Scholar h5-index: 77, TOP 5
Turn off MathJax
Article Contents
Ting Wang, Xiaoquan Xu and Xiaoming Tang, "Scalable Clock Synchronization Analysis: A Symmetric Noncooperative Output Feedback Tubes-MPC Approach," IEEE/CAA J. Autom. Sinica, vol. 7, no. 6, pp. 1604-1626, Nov. 2020. doi: 10.1109/JAS.2020.1003363
Citation: Ting Wang, Xiaoquan Xu and Xiaoming Tang, "Scalable Clock Synchronization Analysis: A Symmetric Noncooperative Output Feedback Tubes-MPC Approach," IEEE/CAA J. Autom. Sinica, vol. 7, no. 6, pp. 1604-1626, Nov. 2020. doi: 10.1109/JAS.2020.1003363

Scalable Clock Synchronization Analysis: A Symmetric Noncooperative Output Feedback Tubes-MPC Approach

doi: 10.1109/JAS.2020.1003363
Funds:  The work was supported by the National Natural Science Foundation of China (61972061, 61403055, 51705059, 51605065), the Chongqing Science and Technology Commission (2017jcyjAX0453, cstc2018jcyjAX0691, cstc2018jcyjAX0139), the Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJQN201800645), the Science and Technology Research Program of Chongqing Municipal Education Commission (KJZD-K201900604), and the Chongqing Education Administration Program Foundation of China (KJ1600402)
More Information
  • In the cyber-physical environment, the clock synchronization algorithm is required to have better expansion for network scale. In this paper, a new measurement model of observability under the equivalent transformation of minimum mean square error (MMSE) is constructed based on basic measurement unit (BMU), which can realize the scaled expansion of MMSE measurement. Based on the state updating equation of absolute clock and the decoupled measurement model of MMSE-like equivalence, which is proposed to calculate the positive definite invariant set by using the theoretical-practical Luenberger observer as the synthetical observer, the local noncooperative optimal control problem is built, and the clock synchronization system driven by the ideal state of local clock can reach the exponential convergence for synchronization performance. Different from the problem of general linear system regulators, the state estimation error and state control error are analyzed in the established affine system based on the set-theory-in-control to achieve the quantification of state deviation caused by noise interference. Based on the BMU for isomorphic state map, the synchronization performance of clock states between multiple sets of representative nodes is evaluated, and the scale of evaluated system can be still expanded. After the synchronization is completed, the state of perturbation system remains in the maximum range of measurement accuracy, and the state of nominal system can be stabilized at the ideal state for local clock and realizes the exponential convergence of the clock synchronization system.

     

  • loading
  • [1]
    J. Yick, B. Mukherjee, and D. Ghosal, “Wireless sensor network survey,” Comput. Netw., vol. 52, no. 12, pp. 2292–2330, Aug. 2008. doi: 10.1016/j.comnet.2008.04.002
    [2]
    S. Ganeriwal, R. Kumar, and M. B. Srivastava, “Timing-sync protocol for sensor networks,” in Proc. 1st Int. Conf. Embedded Networked Sensor Systems, Los Angeles, USA, 2003, pp. 138-149.
    [3]
    J. Elson, L. Girod, and D. Estrin, “Fine-grained network time synchronization using reference broadcasts,” in Proc. 5th Symp. Operating Systems Design and Implementation, Boston, USA, 2002, pp. 147-163.
    [4]
    M. Maróti, B. Kusy, G. Simon, Á. Lédeczi, “The flooding time synchronization protocol,” in Proc. 2nd Int. Conf. Embedded Networked Sensor Systems, Baltimore, USA, 2004, pp. 39-49.
    [5]
    L. Schenato, and F. Fiorentin, “Average TimeSynch: A consensus-based protocol for clock synchronization in wireless sensor networks,” Automatica, vol. 47, no. 9, pp. 1878–1886, Jan. 2011. doi: 10.1016/j.automatica.2011.06.012
    [6]
    S. Ahmed, F. Xiao, and T. W. Chen, “Asynchronous consensus-based time synchronisation in wireless sensor networks using unreliable communication links,” IET Control Theory Appl., vol. 8, no. 12, pp. 1083–1090, Aug. 2014. doi: 10.1049/iet-cta.2013.0859
    [7]
    J. P. He, P. Cheng, L. Shi, J. M. Chen, and Y. X. Sun, “Time synchronization in WSNs: A maximum-value-based consensus approach,” IEEE Trans. Autom. Control, vol. 59, no. 3, pp. 660–675, Mar. 2014. doi: 10.1109/TAC.2013.2286893
    [8]
    E. Garone, A. Gasparri, and F. Lamonaca, “Clock synchronization protocol for wireless sensor networks with bounded communication delays,” Automatica, vol. 59, pp. 60–72, Sep. 2015. doi: 10.1016/j.automatica.2015.06.014
    [9]
    S. Bolognani, R. Carli, E. Lovisari, and S. Zampieri, “A randomized linear algorithm for clock synchronization in multi-agent systems,” IEEE Trans. Autom. Control, vol. 61, no. 7, pp. 1711–1726, Jul. 2016. doi: 10.1109/TAC.2015.2479136
    [10]
    F. Lamonaca, A. Gasparri, E. Garone, and D. Grimaldi, “Clock synchronization in wireless sensor network with selective convergence rate for event driven measurement applications,” IEEE Trans. Instrum. Meas., vol. 63, no. 9, pp. 2279–2287, Feb. 2014. doi: 10.1109/TIM.2014.2304867
    [11]
    Y. C. Wu, Q. Chaudhari, and E. Serpedin, “Clock synchronization of wireless sensor networks,” IEEE Signal Process. Mag., vol. 28, no. 1, pp. 124–138, Jan. 2011. doi: 10.1109/MSP.2010.938757
    [12]
    B. Luo and Y. C. Wu, “Distributed clock parameters tracking in wireless sensor network,” IEEE Trans. Wirel. Commun., vol. 12, no. 12, pp. 6464–6475, Dec. 2013. doi: 10.1109/TWC.2013.103013.130811
    [13]
    D. P. Li, Y. J. Liu, S. C. Tong, C. L. P. Chen, and D. J. Li, “Neural networks-based adaptive control for nonlinear state constrained systems with input delay,” IEEE Trans. Cybern., vol. 49, no. 4, pp. 1249–1258, Apr. 2019. doi: 10.1109/TCYB.2018.2799683
    [14]
    D. P. Li, D. J. Li, Y. J. Liu, S. C. Tong, and C. L. P. Chen, “Approximation-based adaptive neural tracking control of nonlinear MIMO unknown time-varying delay systems with full state constraints,” IEEE Trans. Cybern., vol. 47, no. 10, pp. 3100–3109, Oct. 2017. doi: 10.1109/TCYB.2017.2707178
    [15]
    J. M. Chen, Q. Tu, Y. Zhang, H. H. Chen, and Y. X. Sun, “Feedback-based clock synchronization in wireless sensor networks: A control theoretic approach,” IEEE Trans. Veh. Technol., vol. 59, no. 6, pp. 2963–2973, Jul. 2010. doi: 10.1109/TVT.2010.2049869
    [16]
    T. Wang, C. Y. Cai, D. Guo, X. M. Tang, and H. Wang, “Clock synchronization in wireless sensor networks: A new model and analysis approach based on networked control perspective,” Math. Probl. Eng., vol. 2014, pp. 731980, Aug. 2014.
    [17]
    T. Wang, D. Guo, C. Y. Cai, X. M. Tang, and H. Wang, “Clock synchronization in wireless sensor networks: Analysis and design of error precision based on lossy networked control perspective,” Math. Probl. Eng., vol. 2015, pp. 346521, Apr. 2015.
    [18]
    P. Wang and B. C. Ding, “Distributed RHC for tracking and formation of nonholonomic multi-vehicle systems,” IEEE Trans. Autom. Control, vol. 59, no. 6, pp. 1439–1453, Jun. 2014. doi: 10.1109/TAC.2014.2304175
    [19]
    M. A. Müller, M. Reble, and F. Allgöwer, “Cooperative control of dynamically decoupled systems via distributed model predictive control,” Int. J. Robust Nonlinear Control, vol. 22, no. 12, pp. 1376–1397, Aug. 2012. doi: 10.1002/rnc.2826
    [20]
    B. C. Ding and Y. Q. Tang, “A noncooperative distributed model predictive control for constrained linear systems with decoupled dynamics,” in Proc. 34th Chinese Control Conf., Hangzhou, China, 2015, pp. 4084-4090.
    [21]
    B. C. Ding, L. H. Xie, and W. J. Cai, “Distributed model predictive control for constrained linear systems,” Int. J. Robust Nonlinear Control, vol. 20, no. 11, pp. 1285–1298, Jul. 2009. doi: 10.1002/rnc.1512
    [22]
    D. Mayne, “Robust and stochastic model predictive control: Are we going in the right direction?” Annu. Rev. Control, vol. 41, pp. 184–192, May 2016. doi: 10.1016/j.arcontrol.2016.04.006
    [23]
    P. D. Christofides, R. Scattolini, D. M. de la Pena, and J. F. Liu, “Distributed model predictive control: A tutorial review and future research directions,” Comput. Chem. Eng., vol. 51, pp. 21–41, Apr. 2013. doi: 10.1016/j.compchemeng.2012.05.011
    [24]
    D. Q. Mayne, “Model predictive control: Recent developments and future promise,” Automatica, vol. 50, no. 12, pp. 2967–2986, Dec. 2014. doi: 10.1016/j.automatica.2014.10.128
    [25]
    X. M. Tang and B. C. Ding, “Model predictive control of linear systems over networks with data quantizations and packet losses,” Automatica, vol. 49, no. 5, pp. 1333–1339, May 2013. doi: 10.1016/j.automatica.2013.02.033
    [26]
    W. L. He, B. Zhang, Q. L. Han, F. Qian, J. Kurths, and J. D. Cao, “Leader-following consensus of nonlinear multiagent systems with stochastic sampling,” IEEE Trans. Cybern., vol. 47, no. 2, pp. 327–338, Feb. 2017.
    [27]
    W. L. He, G. R. Chen, Q. L. Han, and F. Qian, “Network-based leader-following consensus of nonlinear multi-agent systems via distributed impulsive control,” Inf. Sci., vol. 380, pp. 145–158, Feb. 2017. doi: 10.1016/j.ins.2015.06.005
    [28]
    X. M. Tang, H. C. Qu, P. Wang, and M. Zhao, “Constrained off-line synthesis approach of model predictive control for networked control systems with network-induced delays,” ISA Trans., vol. 55, pp. 135–144, Mar. 2015. doi: 10.1016/j.isatra.2014.11.007
    [29]
    Y. P. Yang, W. L. He, Q. L. Han, and C. Peng, “H Synchronization of networked master–slave oscillators with delayed position data: The positive effects of network-induced delays,” IEEE Trans. Cybern., vol. 49, no. 12, pp. 4090–4102, Dec. 2019. doi: 10.1109/TCYB.2018.2857507
    [30]
    N. Wang, S. F. Su, X. X. Pan, X. Yu, G. M. Xie, “Yaw-guided trajectory tracking control of an asymmetric underactuated surface vehicle,” IEEE Trans. Ind. Inform., vol. 15, no. 6, pp. 3502–3513, Jun. 2019. doi: 10.1109/TII.2018.2877046
    [31]
    N. Wang, S. Su, M. Han, and W. H. Chen, “Backpropagating constraints-based trajectory tracking control of a quadrotor with constrained actuator dynamics and complex unknowns,” IEEE Trans. Syst.,Man,Cybern.:Syst., vol. 49, no. 7, pp. 1322–1337, Jul. 2019. doi: 10.1109/TSMC.2018.2834515
    [32]
    U. Maeder and M. Morari, “Offset-free reference tracking with model predictive control,” Automatica, vol. 46, no. 9, pp. 1469–1476, Sep. 2010. doi: 10.1016/j.automatica.2010.05.023
    [33]
    M. G. Forbes, R. S. Patwardhan, H. Hamadah, and R. B. Gopaluni, “Model predictive control in industry: Challenges and opportunities,” IFAC-PapersOnLine, vol. 48, no. 8, pp. 531–538, Dec. 2015. doi: 10.1016/j.ifacol.2015.09.022
    [34]
    M. Lorenzen, F. Dabbene, R. Tempo, and F. Allgöwer, “Constraint-tightening and stability in stochastic model predictive control,” IEEE Trans. Autom. Control, vol. 62, no. 7, pp. 3165–3177, Jul. 2017. doi: 10.1109/TAC.2016.2625048
    [35]
    L. Chisci, J. A. Rossiter, and G. Zappa, “Systems with persistent disturbances: Predictive control with restricted constraints,” Automatica, vol. 37, no. 7, pp. 1019–1028, Jul. 2001. doi: 10.1016/S0005-1098(01)00051-6
    [36]
    D. Q. Mayne and W. Langson, “Robustifying model predictive control of constrained linear systems,” Electron. Lett., vol. 37, no. 23, pp. 1422–1423, Nov. 2001. doi: 10.1049/el:20010951
    [37]
    D. Q. Mayne, M. M. Seron, and S. V. Rakovic, “Robust model predictive control of constrained linear systems with bounded disturbances,” Automatica, vol. 41, no. 2, pp. 219–224, Feb. 2005. doi: 10.1016/j.automatica.2004.08.019
    [38]
    D. Q. Mayne, S. V. Rakovic, R. Findeisen, and F. Allgöwer, “Robust output feedback model predictive control of constrained linear systems,” Automatica, vol. 42, no. 7, pp. 1217–1222, Jul. 2006. doi: 10.1016/j.automatica.2006.03.005
    [39]
    S. V. Rakovic, “Robust control of constrained discrete time systems: Characterization and implementation,” Ph.D. dissertation, Imperial College London, London, UK, 2005.
    [40]
    S. V. Rakovic, E. C. Kerrigan, K. I. Kouramas, and D. Q. Mayne, “Invariant approximations of the minimal robust positively Invariant set,” IEEE Trans. Autom. Control, vol. 50, no. 3, pp. 406–410, Mar. 2005. doi: 10.1109/TAC.2005.843854
    [41]
    D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, “Constrained model predictive control: Stability and optimality,” Automatica, vol. 36, no. 6, pp. 789–814, Jun. 2000. doi: 10.1016/S0005-1098(99)00214-9
    [42]
    A. Jadbabaie, J. Yu, and J. Hauser, “Unconstrained receding-horizon control of nonlinear systems,” IEEE Trans. Autom. Control, vol. 46, no. 5, pp. 776–783, May 2001. doi: 10.1109/9.920800
    [43]
    M. V. Kothare, V. Balakrishnan, and M. Morari, “Robust constrained model predictive control using linear matrix inequalities,” Automatica, vol. 32, no. 10, pp. 1361–1379, Oct. 1996. doi: 10.1016/0005-1098(96)00063-5

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(15)  / Tables(2)

    Article Metrics

    Article views (1017) PDF downloads(43) Cited by()

    Highlights

    • This paper constructs an observable measurement model under the BMU for absolute clock in the large-scale network from the viewpoint of networked control theory.
    • Aiming at the calculation problem of positive definite invariant sets, the observability measurement model of MMSE-like equivalence is proposed to calculate the positive definite invariant set by using the Luenberger observer as the synthetical observer. Then the on-line calculation of the Tubes-MPC method for clock synchronization can be realized.
    • Using the feedback control strategy and set-theory-in-control to establish the control error positive definite set, quantitatively analyzing the deviation between the estimated system state and the nominal system state with a measurement model of observability. The exponential stability convergence performance of Tubes-MPC for clock synchronization is achieved.
    • The determined estimated value of the absolute state by using the equivalent observability measurement model of MMSE is based on the ideal state as public reference target. The problem of clock synchronization is transformed into the problem of set-point tracking to ideal state for local clock.

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return