熵在随机系统故障诊断和容错控制中的应用

On the Applications of Entropy Concept in the Fault Diagnosis and Tolerant Control for Stochastic Systems

长期以来,关于随机动态系统的故障诊断和容错控制的研究一直是控制理论和应用的重要领域之一。随机控制系统故障诊断的目标是建立有效的故障估计算法以使残差信号方差最小。这种方法仅适用于高斯型残差或者具有对称分布的概率密度函数的残差。然而,对非高斯残差而言,仅使用残差信号的方差不能够全面表示残差的不确定性。针对非高斯随机动态控制系统提出了新的故障诊断和容错控制算法,以使故障诊断中残差信号的熵极小化,同时极小化故障状态下闭环控制系统跟踪误差的熵。

Over the past decades, fault diagnosis and fault tolerant control for dynamic stochastic systems have always been one of theimportant areas of research in control theory and applications. The purpose of fault diagnosis is to obtain effective fault estimation algorithm so that the variance of the residual signals is minimized. Such methods only applicable to Gaussian residuals or the residuals whose probability density functions are of a symetrical distribution shape. However, for non-Gaussian residuals, the embedded uncertainties cannot be fully described by only using their variances. This paper proposes a novel preliminary methodology on fault diagnosis and tolerant control for non-Gaussian dynamic stochastic systems, where the idea is to ensure that the entropy of residual signals for fault diagnosis and the entropy of the closed loop tracking errors are all minimized when the system is subjected to faults.