离散线性系统部分可观测性测试配置

Measurement optimization of linear discrete systems for partial observability

不可观测系统的部分状态可观测性对于大系统故障检测具有十分重要的意义。研究了基于部分可观测性的不可观测离散线性系统测点优化配置问题,证明了采用有限次观测值构造一个矩阵,可以给出部分可观测性成立的充分必要条件,并进一步证明了部分可观测性的度量可以用一个矩阵的秩的特性来刻画。最后,给出了离散线性系统部分可观测性测试优化配置的度量指标。算例表明,提出的部分可观测性度量指标具有简单实用的特点。

Observability of a part of states （ partial observability） of unobservable system is very important for fault detection of large systems. Measurement points optimization of unobservable linear discrete systems based on partial observability was studied. It was proved that a sufficient and necessary condition of the partial observability can be obtained by a matrix which is formed by limited observations of the system. Then the rank characteristic of a matrix was proved to be able to be applied to express how observable those partial states are. Finally, an index of this partial observability was presented for the measurement optimization.