S-synchronization Structural Identifiability and Identification of Nonlinear Dynamic Systems

Abstract

An approach to the structural identifiability analysis of nonlinear dynamic systems under uncertainty is proposed. We have shown that S-synchronization is the necessary condition for the structural identifiability of a nonlinear system. Conditions are obtained for the design of a model which identifies the nonlinear part of the system. The method is proposed for the obtaining of a set which contains the information on the nonlinear part. A class of geometric frameworks which reflect the state of the system nonlinear part is introduced. Geometrical frameworks are defined on the synthesized set. The conditions are given for the structural indistinguishability of geometric frameworks on the set of S-synchronizing inputs. Local identifiability conditions are obtained for the nonlinear part. We are shown that a non-synchronizing input gives an insignificant geometric framework. This leads to a structural non-identifiability of the system nonlinear part. The method is proposed for the estimation of the structural identifiability the nonlinear part of the system. Conditions for parametric identifiability of the system linear part are obtained. We show that the structural identifiability is the basis for the structural identification of the system. The hierarchical immersion method is proposed for the estimation of nonlinear system structural parameters. The method is used for the structural identification of a system with Bouc-Wen hysteresis.