On metric observers for nonlinear systems

While observer design is well understood and widely used for linear systems, extensions to nonlinear systems have lacked generality. Motivated by fluid dynamics, this paper shows that the use of so-called Euler coordinates in general nonlinear, non-autonomous systems allows major simplifications such as a superposition principle, and leads to new analysis and design methods. A system's dynamic equations may be systematically shaped through a change of metric based on the available measurements, rather than by explicit error feedback. This in turn leads to new deterministic observer design techniques for general nonlinear non-autonomous systems.