A High-Gain Observer for Embedded Polynomial Dynamical Systems

This article deals with the construction of high-gain observers for autonomous polynomial dynamical systems. In contrast to the usual approach, the system's state is embedded into a higher dimensional Euclidean space. The observer state will be contained in said Euclidean space, which has usually higher dimension than the system's state space. Due to this embedding it is possible to avoid singularities in the observation matrix. For some systems this even allows constructing global observers in a structured way, which would not be possible in the lower-dimensional case. Finally, the state estimate in the original coordinates can be obtained by a projection. The proposed method is applied on some example systems.

Automated summary

This article discusses the construction of high-gain observers for autonomous polynomial dynamical systems. Unlike the usual approach, the system's state is embedded into a higher dimensional Euclidean space. The observer state will be contained in this Euclidean space, which has a higher dimension than the system's state space. By using this embedding, singularities in the observation matrix can be avoided and global observers can be constructed in a structured way for some systems, which would not be possible in lower-dimensional cases. Finally, the state estimate in the original coordinates can be obtained through a projection. The proposed method is demonstrated on several example systems.