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Volume 7 Issue 6
Oct.  2020

IEEE/CAA Journal of Automatica Sinica

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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)
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  • 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.

     

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    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.

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