Identifiability of Slowly Varying Systems

A system is conceived of as being slowly varying if it changes slowly enough to permit identification to within a specified error. A generic model is developed to study the identifiability and identification of slowly varying systems. The model is suitable for a large variety of nonlinear, time-varying, causal, bounded memory systems; it has finitely many parameters and is linear in its parameters. Results are obtained with the use of this general model that give guaranteed accuracy of identification as a function of the prior knowledge of the unknown system, the maximum rate of time variation of the system, and the characteristics of output observation noise. To derive these results, a recursive estimation procedure is developed for time-discrete linear dynamical system structures in which the observation noise is statistical but the dynamic equation noise is nonstatistical and is known only to be bounded.