Identifiability and Observability of Nonsmooth Systems via Taylor-Like Approximations

• 成果类型: Article
• 署名作者: Stechlinski, Peter; Eisa, Sameh A.; Abdelfattah, Hesham
• 署名单位: University of Maine System; University of Maine Orono; University System of Ohio; University of Cincinnati; University System of Ohio; University of Cincinnati
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3533366
• 发表日期: 2025
• 页码: 4178-4185
• 关键词: Observability; vectors; sensitivity; meteorology; STANDARDS; Nonlinear systems; Linear approximation; Jacobian matrices; Graphics; Eigenvalues and eigenfunctions; Identifiability; lexicographic derivatives; observability; nonsmooth systems; sensitivity theory; Stommel-box climate model; Taylor-like approximation

摘要

New sensitivity-based methods are developed for determining identifiability and observability of nonsmooth input-output systems. More specifically, lexicographic derivatives are used to construct nonsmooth sensitivity rank condition (SERC) tests, which we call lexicographic SERC (L-SERC) tests. The introduced L-SERC tests are practically implementable, accurate, and analogous to (and indeed recover) their smooth counterparts. To accomplish this, a novel first-order Taylor-like approximation theory is developed to directly treat nonsmooth (i.e., continuous but nondifferentiable) functions. An L-SERC algorithm is proposed that determines partial structural identifiability or observability, which are useful characterizations in the nonsmooth setting. Lastly, the theory is illustrated through an application in climate modeling.