带有色噪声和一步观测滞后的广义控制系统时变估值器

Time-varying estimator for descriptor control system with colored noise and one-step measurement delay

对于带有色过程噪声和一步随机观测滞后的线性离散随机广义控制系统,提出了基于Klaman滤波理论的时变估值算法。利用奇异值分解方法将原广义控制系统转化为两个降阶正常子系统,利用状态扩维方法和去随机化方法,将一步观测滞后和有色过程噪声都压缩到新模型的虚拟过程噪声和虚拟观测噪声中,从而得到增广降阶状态的标准状态空间模型。对于该标准系统,利用经典Kalman滤波理论,得到了该增广降阶状态的时变Kalman估值器(包括Kalman滤波器、预报器和平滑器)。利用增广降阶状态和广义系统原状态之间的关系,提出了广义控制系统的时变估值器及其估值误差方差阵。通过双循环电路系统的仿真实例验证了所提出算法的有效性和正确性。

For the linear discrete stochastic descriptor control system with colored process noise and one-step measurement delay, the time-varying estimator is presented based on the Kalman filtering. The original descriptor control system is transformed to two reduced-order standard subsystems by the Singular value decomposition(SVD) approach. Applying the state augmented approach and the de-randomization approach, the colored process noise and one-step measurement delay are all compressed into the fictitious process noise and fictitious measurement noise. The standard state space model for the augmented reduced-order state is obtained. Applying the classical Kalman filtering theory, the time-varying Kalman estimator of the augmented reduced-order is presented. Further, the time-varying estimator of the descriptor control system is presented according to the relation of the augmented reduced-order state and the original state of the descriptor control system. The simulation example about double-loops circuit system is shown to verify the effectiveness and correctness of the presented algorithm.