观测信息非完整未知输入系统估计问题研究

The estimation problems for systems with unknown inputs have been widely applied in the fields of traffic systems, weather forecast, and so on. The estimation for systems with unknown inputs is very challenging in theory due to the existence of the completely/partially unobserved unknown inputs and random packet dropout uncertainty induced by network. Firstly, the simultaneous input and state estimation problem for systems with completely unobserved unknown inputs and random packet dropout will be considered in this project. A novel estimator which has a different performance index compared with previous estimators will be proposed based on the time-stamp technique, and the random packet dropout rate which influences the mean square stability of the estimator will be analyzed. Secondly, the estimation problem for periodic systems with completely unobserved unknown inputs and random packet dropout will be studied, the convergence conditions of the periodic Riccati equation will be sought, and the effective design scheme for periodic estimator will be provided. Thirdly, the more general estimation problem will be considered for systems with partially observed unknown inputs and random packet dropout, and the unified design approach to the estimator will be presented. Finally, based on the systems with unknown inputs, the optimal sensor collaboration policy for parameter tracking using energy harvesting sensors will be explored: based on the closed relationship between random packet dropout and sensor network, the approach which is effective to deal with the estimation for systems with unknown inputs and random packet dropout will be applied to the sensor network and the collaboration policy will be proposed such that the tracking performance is optimal. The results of this project will further improve the estimation theory for systems with unknown inputs.

含未知输入系统估计问题在交通系统及天气预报等领域具有广泛应用。由于未知输入完全不可观测/部分不可观测及网络引起的随机丢包不确定性，导致未知输入系统估计在理论上存在很大挑战性。本项目首先考虑系统含有随机丢包及完全不可观测未知输入情形下的输入和状态同时估计问题，基于时间戳技术提出与已有估计器性能指标不同的新型估计器，分析随机丢包率对估计器均方稳定性的影响。其次，研究具有随机丢包和完全不可观测未知输入周期系统估计问题，寻求周期黎卡提方程的收敛条件，提供周期估计器的有效设计方案。然后，考虑更一般的具有随机丢包且未知输入部分可观测的估计问题，给出估计器的统一设计方法。最后，基于未知输入系统，探求面向参数跟踪的能量收集传感器协作策略：基于随机丢包与传感器网络的紧密关系，将具有随机丢包的未知输入系统估计的有效方法应用到传感器网络，提出协作策略实现跟踪性能最优。本课题的研究将进一步完善未知输入系统理论。

含未知输入系统估计问题在交通系统及天气预报等领域具有广泛应用。由于未知输入完全不可观测性及网络系统引起的随机丢包不确定性，导致未知输入系统估计在理论上存在很大挑战性。本项目首先考虑了系统含有随机丢包及完全不可观测未知输入情形下的输入和状态同时估计问题，基于时间戳技术提出了与已有估计器性能指标不同的新型估计器，分析了随机丢包率对估计器均方稳定性的影响。其次，研究了具有随机丢包和完全不可观测未知输入周期系统估计问题，得到了周期黎卡提方程的收敛条件，提供了周期估计器的有效设计方案。然后，基于观测丢包系统，探求了面向参数跟踪的传感器协作策略：基于随机丢包与传感器网络的紧密关系，将具有随机丢包系统估计的有效方法应用到传感器网络，提出了带有约束条件的协作策略实现跟踪性能最优。最后，针对含非高斯噪声的观测丢包系统，提出了最大熵卡尔曼估计器的有效设计方法。本课题的研究成果将对随机系统、未知输入系统最优估计问题的研究产生积极的推动作用。