A Spectral Decomposition Identification Algorithm for Structured State-Space Models: Estimating Semiphysical Models of Social Cognitive Theory

Structured state-space (grey-box) identification using experimental input-output data remains the desired framework for modeling dynamic physical and semiphysical systems represented by (or simplified to) a set of linear differential equations of a predetermined structure. While grey-box models can rise with favorable statistical properties, solver initialization of classical methods and structural identifiability often pose a challenge to the user seeking satisfactory results. By assuming distinct poles and Zero-Order Hold intersample behavior of the underlying system, it is shown that the typical grey-box constrained optimization problem can be formulated into an easier one by solving constrained eigenvalue problems. Following the trend of existing literature, the proposed formulation relies on a consistent discrete-time black-box model (e.g., N4SID) to solve for a structured, continuous-time one. While can be entirely sufficient in easier cases, this method is best suited for initializing the classical prediction-error estimation method, hence relieving the user from the burden of solver initialization in the absence of prior knowledge.