Computing Measures of Identifiability, Observability, and Controllability for a Dynamic System Model with the StrucID App. Issue 7 (2021)

• Record Type: Journal Article
• Authors: Stigter, J.D.; Joubert, D.
• Is Part Of: IFAC-PapersOnLine. Volume 54:Issue 7(2021)
• Page Start: 138
• Page End: 143
• Publication Date: 2021
• Subjects: Identifiability -- Observability -- Controllability -- Sensitivity Analysis; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2021.08.348
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: Identifiability, observability, and controllability are important structural properties of a dynamic system model. Our interest lies in the detection of a lack of identifiabil-ity/observability and/or controllability through the computation and subsequent analysis of the exact nullspace of the gramian for non-linear systems. For this analysis we have developed a user-friendly application with the name StrucID which runs in Matlab. The StrucID App requires as input a model definition in (possibly non-linear) state space format. In addition, an output equation that may also be non-linear is required. Through a rank test (SVD) on an associated sensitivity matrix, so-called signature graphs are produced. These represent a model's singular values and nullspace vectors and provide a visual summary. The results can now be used in a substantially reduced symbolic computation (not included yet in the current version of StrucID) that computes a Fliess series expansion of the output signal to arrive at the nullspace of an associated Jacobi matrix. Solving an underlying partial differential equation then completes the structural analysis and generates a re-parametrisation and/or state transformation that allows for model reduction in an exact manner. A few examples will be presented.