Job offer

For most real-world dynamical systems, input-output models are developed for control, optimization, prediction, or diagnosis. However, the system dynamics are often unknown. Data-driven modeling, combining system identification and machine learning techniques, provides an effective strategy to determine a model from input-output data collected during excitation experiments. The user selects a structure that groups several candidate models. These models are ranked according to their ability to explain the data. The identified model is the one with the optimal score. In the current era of Big Data, many studies are now considering the use of large number of data in order to obtain the most accurate model. However, having a large dataset is not enough in practice! Indeed, an inappropriate choice of excitation may lead to ambiguity: several different models may achieve the same score, making the identification incorrect and potentially leading to dangerous scenarios if the model is later used for diagnosis or control.

The property that guarantees the uniqueness of the optimal model is called data informativity. It indicates whether the data contain sufficient information about the system dynamics. Introduced in the 1980s [5], this concept led to the establishment of necessary and sufficient conditions on excitation for the identification of linear time-invariant (LTI) systems [1-4]. However, these studies focused on the asymptotic case, assuming an infinite amount of data, which is unrealistic. More recently, informativity has been studied in the context of a finite number of data points [7,8], either in the noise-free case (using Willems' lemma [9]) or with deterministic and bounded noise (set-membership method [8]). In practice, these assumptions are rarely satisfied since noise is often stochastic.

The central question of this thesis is the development of necessary and sufficient conditions on excitation to guarantee the informativity of a finite number of data affected by stochastic noise, in the framework of linear system identification. The approach proposed in a recent work at CRAN [6] will be used as a starting point. However, the simplifying assumptions in [6] limit its applicability. The objective is therefore to extend the analysis to more general scenarios, particularly closed-loop identification and linear parameter-varying systems, which are better suited for complex systems.

References

[1] Bazanella et al., "Necessary and sufficient conditions for uniqueness of the minimum in prediction error identification," Automatica, 48(8):1621-1630, 2012.

[2] Colin et al., "Closed-loop identification of MIMO systems in the prediction error framework: Data informativity analysis," Automatica, 121:109171, 2020.

[3] Colin et al., "Data informativity for the open-loop identification of MIMO systems in the prediction error framework," Automatica, 117:109000, 2020.

[4] Gevers et al., "Informative data: How to get just sufficiently rich?," Proceedings of the 47th IEEE Conference on Decision and Control, pp.1962-1967, 2008.

[5] Ljung, System Identification: Theory for the User, Prentice Hall, 1999.

[6] Sleiman et al., "Data informativity for prediction error identification of stochastic LTI systems with repeated finite-time experiments in open-loop," 2025.

[7] van Waarde et al., "A behavioral approach to data-driven control with noisy input-output data," IEEE Transactions on Automatic Control, 69(2):813-827, 2023.

[8] van Waarde et al., "Data informativity: A new perspective on data-driven analysis and control," IEEE Transactions on Automatic Control, 65(11):4753-4768, 2020.

[9] Willems et al., "A note on persistency of excitation," Systems & Control Letters, 54(4):325-329, 2005.

Funding category: Contrat doctoral

PHD title: Doctorat en Automatique (Ph.D. in Automatic Control)

Specific Requirements

We are looking for a candidate who has graduated or is in the final year of a Master's program or an engineering school degree with skills in control engineering, system identification, data analysis, machine learning or applied mathematics. A good level of English (min B2) is required and proficiency in French is not mandatory.