SET-MEMBERSHIP IDENTIFIABILITY OF NONLINEAR MODELS AND RELATED PARAMETER ESTIMATION PROPERTIES

Identifiability guarantees that the mathematical model of a dynamic system is well defined in the sense that it maps unambiguously its parameters to the output trajectories. This paper casts identifiability in a set-membership (SM) framework and relates recently introduced properties, namely, SM-identifiability, mu-SM-identifiability, and epsilon-SM-identifiability, to the properties of parameter estimation problems. Soundness and epsilon-consistency are proposed to characterize these problems and the solution returned by the algorithm used to solve them. This paper also contributes by carefully motivating and comparing SM-identifiability, mu-SM-identifiability and epsilon-SM-identifiability with related properties found in the literature, and by providing a method based on differential algebra to check these properties.