具有噪声方差及多种网络诱导不确定系统鲁棒Kalman估计

Robust Kalman estimation for system with uncertainties of noise variances and multiple networked inducements

对不确定噪声方差乘性噪声,同时带观测缺失、丢包和一步随机观测滞后三种网络诱导特征的混合不确定网络化系统,应用带虚拟噪声的扩维方法和去随机参数方法,将其转化为带不确定虚拟噪声方差的时变系统.基于极大极小鲁棒估计原理,对带虚拟噪声方差保守上界的最坏情形系统,设计了鲁棒时变和稳态Kalman估值器.对所有容许的不确定性,保证实际Kalman估计误差方差有最小上界.应用扩展的Lyapunov方程方法和矩阵分解方法证明了所设计估值器的鲁棒性.证明了实际和保守估值器的精度关系,以及时变和稳态估值器间的按实现收敛性.应用于F-404航空发动机系统的仿真验证了所提出结果的正确性和有效性.

By using the augmented method with fictitious noise and derandomization approach,the networked mixed uncertain system with uncertain variances-multiplicative noises,and three networked induced features,including missing measurement,packet dropouts and one-step random measurement delay,is converted into time-varying system with uncertain fictitious noise variances.Then,based on the minimax robust estimation principle,the robust time-varying and steady-state Kalman estimators are designed for worst-case system with conversative upper bound of fictitious noise variances.For all admissible uncertainties,the actual Kalman estimation error variances are guaranteed to have minimal upper bounds.The robustness of designed estimators is proved by extended Lypunov equation method and matrix decomposition method.The accuracy relations between actual and conservative estimators,and the convergence in a realization between time-varying and steady-state are proved.A numerical example used to F-404 aircraft engine system shows the correctness and effectiveness of the proposed results.