随机参数误差的线性系统鲁棒状态估计.pdfVIP

随机参数误差的线性系统鲁棒状态估计 1,2 1,3 刘华波 ，周彤 1 清华大学自动化系，北京　100084 2 青岛大学自动化工程学院，青岛　266071 3 清华大学信息科学与技术国家实验室，北京　100084 摘要：本文研究了一类不确定线性系统的状态估计问题，随机的参数误差可以任意地影响系统 的状态空间模型。基于估计误差的期望最小得到一个形式类似于卡尔曼滤波器的鲁棒状态估计 器，且以与之媲美的计算复杂度递归实现。在较少的假设条件下，该鲁棒状态估计器收敛到一 个稳定的系统，估计误差的协方差矩阵是有界的，且该估计器是渐近无偏的。数值仿真显示本 文所提的鲁棒状态估计器可以取得与已有鲁棒状态估计器相当的估计性能，且应用范围更广。 关键词：状态估计，鲁棒性，回归估计，参数模型误差，正则最小二乘 中图分类号：TP13 Robust state estimation for uncertain linear systems with random parametric uncertainties LIU Hua-Bo1,2 , ZHOU Tong1,3 1 Department of Automation, Tsinghua University, Beijing 100084 2 College of Automation Engineering, Qingdao University, Qingdao 266071 3 TNList, Tsinghua University, Beijing 100084 Abstract: In this paper, we investigate state estimations of a dynamical system with random parametric uncertainties which may arbitrarily affect a state-space plant model. A robust estimator is derived based on expectation minimization of estimation errors. An analytic solution similar to that of the well-known Kalman filter is derived for this new robust estimator which can be realized recursively with a comparable computational complexity. Under some weak assumptions, it is proved that this estimator converges to a stable system, the covariance matrix of estimation errors is bounded, and the estimation is asymptotically unbiased. Numerical simulations show that the obtained robust filter has an estimation accuracy comparable to other estimators and can be applied in a wider range. Foundations: This work was financially supported in part by the 973 Program under Grant 2012CB316504 and 2009CB320602, and by the National Natural Science Foundation of China under Grants 6117412