Abstract:The dynamic behavior of numerous engineering processes is effectively characterized through differential-algebraic equations (DAEs), commonly referred to as descriptor systems. While substantial progress has been achieved in identifying dynamic models governed by ordinary differential equations (ODEs), limited research has addressed the identification of descriptor systems from measured data. This work presents a systematic methodology for identifying the DAE model of a linear descriptor system in discrete difference equation form under errors-in-variables (EIV) setting, where both input and output measurements are corrupted by random noise. The proposed methodology generalizes the identification framework to handle scenarios where the system contains multiple algebraic and different ordered differential relations. The key innovation involves a partial stacking procedure of lagged data matrix with a sequentially increasing lag window that identifies all the differential relations individually. This is preceded by an iterative estimation of the measurement error covariance matrix that is diagonal and heteroskedastic, under large sample conditions. The algorithm simultaneously estimates the number of differential and algebraic relations, observability indices and delay parameters of the differential equations, and all the model coefficients directly from measured data without requiring prior specification from the user. The framework addresses the increased complexity arising from multiple dynamic coupled interactions while maintaining computational tractability through systematic decomposition of the identification problem. Effectiveness of the proposed methodology is demonstrated through several simulation studies.
From: Deepanjhan Das [view email]
[v1]
Mon, 22 Jun 2026 19:32:57 UTC (447 KB)
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