On the solvability of parameter estimation-based observers for nonlinear systems

Parameter estimation-based observer (PEBO) is a recently developed constructive tool to design state observers for nonlinear systems. It reformulates the state estimation problem as one of online parameter identification, effectively addressing many open estimation challenges in practical applications. The feasibility of a PEBO design relies on two fundamental properties: transformability and identifiability. The former pertains to the existence of an injective solution to a suitable partial differential equation, whereas the latter characterizes the uniqueness of the parameterization induced by the resulting nonlinear regression model. In this paper, we analyze the existence of PEBOs for general nonlinear systems by studying these two properties in detail and by providing sufficient conditions under which they hold.