Recursive Identification Algorithms as Nonlinear Systems: Parameter Identifiability and Controllability

Abstract

In this paper we examine parameter identifiability of a system modeled by a linear regression (ARX model). We regard recursive identification algorithms, designed to estimate the parameters of the given linear model, as discrete time nonlinear systems. The output of a nonlinear system representing a recursive parameter estimation algorithm will be the vector of parameter estimates, and its input will be the observed data taken from the system being identified. First, we examine the nonlinear system and obtain a characterization of its controllability. We next link parameter identifiability of the ARX model with a probabilistic version of controllability of this nonlinear stochastic system. We obtain a necessary and sufficient condition for parameter identifiability of the model in a probabilistic context. This condition is given in terms of properties of the chosen algorithm.