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.

中文翻译：

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可扩展的时钟同步分析：对称的非合作输出反馈管-MPC方法

在网络物理环境中，需要时钟同步算法来更好地扩展网络规模。本文在基本测量单位（BMU）的基础上，构建了最小均方误差（MMSE）等效变换下的可观测性测量模型，可以实现MMSE测量的规模扩展。基于绝对时钟的状态更新方程和类似MMSE的等效解耦测量模型，提出以理论上实用的Luenberger观测器作为综合观测器来计算正定不变集，从而解决了局部非合作最优控制问题。内置，并且由本地时钟的理想状态驱动的时钟同步系统可以达到指数收敛，从而实现同步性能。与一般线性系统调节器的问题不同，在建立的仿射系统中，基于控制集理论分析状态估计误差和状态控制误差，以量化噪声干扰引起的状态偏差。基于同构状态图的BMU，可以评估多组代表节点之间时钟状态的同步性能，并且仍可以扩展被评估系统的规模。同步完成后，扰动系统的状态保持在测量精度的最大范围内，标称系统的状态可以稳定在本地时钟的理想状态，实现时钟同步系统的指数收敛。在建立的仿射系统中，基于控制理论，分析了状态估计误差和状态控制误差，实现了对噪声干扰引起的状态偏差的量化。基于同构状态图的BMU，可以评估多组代表节点之间时钟状态的同步性能，并且仍可以扩展被评估系统的规模。同步完成后，扰动系统的状态保持在测量精度的最大范围内，标称系统的状态可以稳定在本地时钟的理想状态，实现时钟同步系统的指数收敛。在建立的仿射系统中，基于控制论，对状态估计误差和状态控制误差进行了分析，以量化噪声干扰引起的状态偏差。基于同构状态图的BMU，可以评估多组代表节点之间时钟状态的同步性能，并且仍可以扩展被评估系统的规模。同步完成后，扰动系统的状态保持在测量精度的最大范围内，标称系统的状态可以稳定在本地时钟的理想状态，实现时钟同步系统的指数收敛。