Sensitivity Matrices as Keys to Local Structural System Properties of Large-Scale Nonlinear Systems.

Abstract Sensitivities are shown to play a key role in a very efficient algorithm, presented in this paper, to establish three fundamental structural system properties: local structural identifiability, local observability and local strong accessibility. Sensitivities have the advantageous property to be governed by linear dynamics, also if the system itself is nonlinear . By integrating their linear dynamics over a short time period, and by sampling the result, a sensitivity matrix is obtained. If this sensitivity matrix satisfies a rank condition, then the local structural system property under investigation holds. This rank condition will be referred to in this paper as the sensitivity rank condition (SERC). Applying a singular value decomposition (SVD) to the sensitivity matrix not only determines its rank but also pinpoints exactly the system components causing a possible failure to satisfy the local structural system property. The algorithm is very efficient because integration of linear systems over short time-periods and computation of an SVD are computationally cheap. Therefore, it allows for the handling of large-scale systems in the order of seconds, as opposed to conventional algorithms that mostly rely on Lie series expansions and a corresponding Lie algebraic rank condition (LARC). We extensively discuss the (dis)advantages of both algorithms and to which extent their results coincide. A series of examples is presented to illustrate these results.