An Efficient Method to Assess Local Controllability and Observability for Non-Linear Systems

摘要

Controllability and observability are two fundamental system properties that yield insight in the structural relationships between state-, input-, and output variables. It is well-known that for non-linear type of system models these structural properties are difficult to analyse, especially if the size of the corresponding model is large. A sensitivity based method to assess local controllability and observability for non-linear systems in a simple way is discussed here and its validity is demonstrated with some examples taken from various applications in the control literature. A major advantage of our sensitivity based approach is that no Lie-derivatives or Lie-brackets have to be calculated and this results in a fast algorithm for structural system analysis. An optional second step in the analyses is the verification of a lack of observability/controllability, once obtained in the first step, with a simplified symbolic computation. Finally, the so-called observability- and controllability signatures of a given system are presented that characterize local observability/controllability and yield a succinct visual summary of these fundamental system properties.