Abstract
In the industrial cyber-physical environment, the performance of clock synchronization with loss of data packets should be analyzed quantitatively. The localized state estimator and controller are designed to realize the speed of convergence for exponential stability of the clock synchronization for the output feedback tubes-model predictive control (Tubes-MPC) of the state-space model. The upper and lower bounds for the variance of synchronization error under the statistical significance were quantitatively analyzed in incomplete measurement. The set of interference error in complete measurement was added into the set of additional estimated errors introduced by packet loss. Clock synchronization of the output feedback Tubes-MPC which has been constructed still has the performance of robust exponential convergence under networked packet loss, and it can be extended to an absolute state-space model with network-level in a unified approach.
Highlights
WHEN clock synchronization is completed in unreliable WSN [1], [2], [4], a lot of data packets with time message cannot successfully arrive in the specified observation period in the process of two-ways message observation, which is called incomplete measurement
The problem is that the random measurement variance introduced by the incomplete measurement will generate additional estimated error [4]–[6], resulting in clock synchronization error and convergence performance of network-level clock cannot be evaluated quantitatively
In IV-D of this paper, we have proved that when there is packet loss and the arrival rate λ satisfies λc < λ ≤ 1, the state of system with the output feedback model predictive control will converge exponentially to the positive invariant set centered at the target point Z
Summary
WHEN clock synchronization is completed in unreliable WSN [1], [2], [4], a lot of data packets with time message cannot successfully arrive in the specified observation period in the process of two-ways message observation, which is called incomplete measurement. This method is independent of networked nodes distribution and method of communication, it is a systematic method which can adapt to networked changes. Considering the loss of observed value, we need to re-establish the estimated model of Kalman filter, analyze the iterative process of error covariance, and discuss the arrival rate λ and convergence of expectation for covariance matrix. Set Sestablishes relationship of set constraint between estimated system and nominal system
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