Public Thesis Defense of Antoine LEGAT - ICTEAM
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Generic Local Identifiability in Dynamic Networks : from Algebraic Characterization to Algorithms for Signal Selection by Antoine LEGAT -
Wednesday, 17 September 2025 at 4:15 p.m. - Room BARB94 - Place Sainte-Barbe - 1348 Louvain-la-Neuve
This thesis investigates the problem of identifiability in linear dynamic networks under partial excitation and measurement. In many practical scenarios, it is infeasible or costly to excite and measure all nodes in a network. Consequently, a central question arises: Which nodes should be excited and measured to ensure that the internal structure of the network can still be identified? We address this question through a three-pronged approach that combines algebraic analysis, graph-theoretic insight, and algorithmic design.
The first main contribution of the thesis 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 of the thesis focuses on the synthesis problem: selecting excitation and measurement sets 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.
Jury members
- Prof. Julien M. Hendrickx (UCLouvain) (Supervisor)
- Prof. Charles Pecheur (UCLouvain) (Chairperson)
- Prof. Pierre-Antoine Absil (UCLouvain) (Secretary)
- Prof. Paul Van den Hof (Eindhoven University of Technology, Netherlands)
- Dr Federica Garin (Inria Grenoble, France)
- Prof. Bahman Gharesifard (Queen’s University, Canada)