主要考虑了具有数据包丢失的网络控制系统(NCSs)的估计问题。首先,给出经典的卡尔曼滤波估计器和协方差矩阵。当量测方程带有噪声时,通过递推的方法严格推导出最优估计(条件期望)。另外,根据系统丢包行为能否被观测到的估计问题,分情况进行讨论。最后,在实际应用中开发了一个次优的近似估计器。这对在大的有限域下研究具有数据包丢失的网络控制系统有所帮助,也为进一步分析网络控制系统的问题提供了研究方向。
In this paper, we mainly investigated the estimation of networked control systems (NCSs) with packet losses. Firstly, we introduced the classical Kalman filter estimator and the covariance matrix. When the measurement equation is with noise, we give the optimal estimator. The optimal estimator is strictly calculated by the recursive method. Moreover, according to whether the packet loss process can be observed, we discussed the estimation problem. Finally, for the application, a simple sub-optimal approximation estimator was developed. It will be helpful to study the NCSs with packet losses in large finite horizon, and provides the research direction for further analyzing the problem of NCSs.
[1] Yang T C. Networked control system: a briefsurvey[J]. Control Theory and Applications, IEE Proceedings, 2006, 153(4): 403412.
[2] Hespanha J P, Naghshtabrizi P, Xu Y. A survey of recent results in networked control systems[J]. Proceedings of the IEEE, 2007, 95(1): 138162.
[3] Seiler P,Sengupta R. Analysis of communication losses in vehicle control problems[C]// American Control Conference, Proceedings of the 2001. Arlington, VA, USA: IEEE, 2001: 14911496.
[4] Meng C, Wang T M, Chou W S, et al. Remote surgery case: robot-assisted teleneurosurgery[C]// IEEE International Conference on Robotics & Automation. New Orleans, LA, USA: IEEE, 2004: 818823.
[5] Elia N. Remote stabilization over fading channels[J]. Systems & Control Letters, 2005, 54(3): 237249.
[6] Qi Q Y, Zhang H S. Output feedback control and stabilization for multiplicative noise systems with intermittent observations[J]. IEEE Transactions on Cybernetics, 2018, 48(7): 2128.
[7] Zhang H S, Xie L. Control and estimation of systems with input/output delays[DB/OL]. [20200624].https://xueshu.baidu.com/usercenter/paper/show?paperid=cd431a7ffa97057ab77c40cf47ad1bc6&site=xueshu_se.
[8] Kalman R E. A new approach to linear filtering and predicted problems[J]. Basic Eng, 1960, 82(1): 3545.
[9] Kalman R E. New results in linear filtering and prediction theory[J]. Basic Eng, 1961, 83(1): 95108.
[10] Nahi N. Optimal recursive estimation with uncertain observation[J]. IEEE Transactions on Information Theory, 1969, 15(4): 457462.
[11] Fortmann T E, Bar-Shalom Y, Scheffe M, et al. Detection thresholds for tracking in clutter-a connection between estimation and signal processing[J]. IEEE Transactions on Automatic Control, 1985, 30(3): 221229.
[12] Sinopoli B, Schenato L, Franceschetti M, et al. Kalman filtering with intermittent observations[J]. IEEE Transactions on Automatic Control, 2004, 1(9):14531464.
[13] Imer O C. Optimal control of LTI systems over unreliable communication links[J]. Automatica, 2006, 42(9): 14291439.
[14] Qi Q Y, Zhang H S. Output feedback control and stabilization for networked control systems with packet losses[J]. IEEE Transactions on Cybernetics, 2016, 47(8): 22232234.
[15] Zhang H, Song X, Shi L. Convergence andmean square stability of suboptimal estimator for systems with measurement packet dropping[J]. IEEE Transactions on Automatic Control, 2012, 57(5): 12481253.
[16] Jacobson V. Congestion avoidance andcontrol[J]. Acm Sigcomm Computer Communication Review, 1988, 18(4): 314329.
[17] Ma X, Qi Q, Zhang H. Optimaloutput feedback control and stabilization for NCSs with packet dropout and delay: TCP case[J]. Journal of Systems ence & Complexity, 2018, 31(1): 147160.
[18] Postel J B. User Datagram Protocol[M]. US: RFC Editor, 1980.
[19] Epstein M, Shi L, Murray R M. An Estimationalgorithm for a class of networked control systems using UDP-like communication schemes[C]// Proceedings of the IEEE Conference on Decision and Control. San Diego, CA, USA: IEEE, 2006: 55975603.
[20] Schenato L, Sinopoli B, Franceschetti M, et al. Foundations of control and estimation over lossy networks[J]. Proceedings of the IEEE, 2007, 95(1): 163187.
[21] Zhang W A, Li Y. Modelling and control of networked control systems with both network-induced delay and packet-dropout[J]. Automatica, 2008, 44(12): 32063210.
[22] Qi Q, Zhang H,Ji Z. Further results on stabilization for NCSs with packet losses and transmission delay: UDP case[J]. Journal of the Franklin Institute, 2019, 356(8): 46014621.
[23] Mo Y L, Garone E, Sinopoli B. LQG control with Markovian packet loss[C]// 2013 European Control Conference. Zurich, Switzerland: IEEE, 2013: 23802385.
[24] Brian D O A, John B M. Optimal Filtering[M]. NJ: Prentice-Hall, Englewood Cliffs, 1979.
