Generic local identifiability in dynamical networks : from algebraic characterizationto algorithms for signal selection
(2025)
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- Authors
- Supervisors
- Hendrickx, Julien
- Abstract
- This thesis investigates identifiability in linear dynamic networks with partial excitation and measurement, using a threefold approach that combines algebraic analysis, graph-theoretic insight, and algorithmic design. The first main contribution is an algebraic characterization of generic local identifiability. We show that, generically, analyzing networks with scalar modules is equivalent to working with analytic transfer functions, which significantly simplifies the analysis. Using tools from manifold theory, we derive necessary and sufficient conditions for local identifiability and demonstrate that this property is pseudo-generic. This leads to a practical algorithm that tests identifiability with probability one by evaluating algebraic conditions on a randomly sampled network instances. We then explore how this algebraic characterization can be translated into graph-theoretic terms. We develop a combinatorial characterization of identifiability based on walk structures in the network, derive walk-based identifiability conditions and introduce the Meta-Walk Graph, a novel graph whose vertices represent bijective walk collections. This combinatorial framework provides a powerful lens for understanding identifiability and guides the design of algorithms. The final part focuses on the synthesis problem: selecting excitations and measurements that guarantee identifiability while minimizing the number of signals used. We prove that finding the optimal solution to this problem is NP-hard, motivating the development of heuristic algorithms. Leveraging the algebraic and combinatorial tools developed earlier, we propose several algorithms that balance computational efficiency with solution quality.
- Affiliations
UCLouvain SST/ICTM/INMA - Pôle en ingénierie mathématique
Citations
Legat, A. (2025). Generic local identifiability in dynamical networks : from algebraic characterizationto algorithms for signal selection. https://hdl.handle.net/2078.5/256546