Computing Measures of Identifiability, Observability, and Controllability for a Dynamic System Model with the StrucID App. Issue 7 (2021) - Stigter, J.D.; Joubert, D.
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.