Identifiability and Observability of Nonsmooth Systems via Taylor-like Approximations

TL;DR

This paper introduces a novel sensitivity-based approach using lexicographic calculus to determine the identifiability and observability of nonsmooth systems, providing practical and accurate tools that directly handle nonsmoothness without smoothing.

Contribution

The paper develops the first Taylor-like approximation theory for nonsmooth systems and proposes L-SERC tests for practical identifiability and observability analysis.

Findings

L-SERC tests are practical and scalable.

The approach accurately handles nonsmoothness without smoothing.

Application demonstrated in climate modeling.

Abstract

New sensitivity-based methods are developed for determining identifiability and observability of nonsmooth input-output systems. More specifically, lexicographic calculus is used to construct nonsmooth sensitivity rank condition (SERC) tests, which we call lexicographic SERC (L-SERC) tests. The introduced L-SERC tests are: (i) practically implementable and amenable to large-scale problems; (ii) accurate since they directly treat the nonsmoothness while avoiding, e.g., smoothing approximations; and (iii) analogous to (and indeed recover) their smooth counterparts. To accomplish this, a first-order Taylor-like approximation theory is developed using lexicographic differentiation to directly treat nonsmooth functions. A practically implementable algorithm is proposed that determines partial structural identifiability or observability, a useful characterization in the nonsmooth setting. Lastly, the theory is illustrated through an application in climate modeling.