Subject Ph. D.

Context Fault diagnosis and fault-tolerant control (FTC) are key issues. Indeed, FDI (fault detection and isolation) or fault diagnosis allows to detect, locate and possibly quantify one or more malfunctions in a process. The fault-tolerant control relies on the results provided by the diagnosis to ensure a certain level of performance despite the occurrence of fault(s) [Ding, 2020]. While these tools have been developed in the linear framework for several decades, the current challenge remains their extension to the nonlinear framework, which is necessary for an accurate description of complex processes. In this perspective, the use of linear parameter varying systems (LPV) [Briat, 2015, Marx, 2019], or polytopic or TS systems [Bainier, 2024a, Takagi, 1985] is an interesting and generic tool for representing a large class of nonlinear systems by a structure close to the linear case or defined by a set of linear submodels [Bernal, 2023, Lendek, 2010]. This representation facilitates the performance analysis and the synthesis of control, observation and diagnostic modules using, for example, optimization under linear matrix inequality constraints (LMI).

Expected researches The cause and nature of the faults affecting the process to be diagnosed and/or controlled have a significant influence on the diagnosis or FTC techniques to be used. Faults can be caused - among other things - by accidental or malicious corruptions of measures taking the form of unknown entries replacing the transmitted data or by transmission defects (missing data, saturations, dead zones, etc) [Bainier, 2024b, Pan, 2023, Bezzaoucha, 2016, Pasqualetti, 2013]. From the modeling point of view, two main classes of faults can be distinguished: additive and parametric. Among the latter, a particular care should be taken with input saturations that prevent the calculated control input from being applied to the system [Tarbouriech, 2011]. Several works have already been done in this direction [Bainier, 2024c, Bainier, 2024b, Bezzaoucha, 2016], but some obstacles still remain (restrictive assumptions, pessimism of the results, etc.) and limit their applications. A new description of the saturation phenomena has been provided in [Bainier, 2024c, Bainier, 2024b] and it should be interesting to consider it for fault detection and isolation in the presence of actuator saturations. Constraints on state variables should also be included to take into account the validity domain of the polytopic rewriting of the original nonlinear model [Nguyen, 2021]. In the context of diagnosis and tolerance to additive faults, an interesting research direction would be to avoid the exclusive use of observer-based structures. Indeed, the observer is synthesized by minimizing the fault influence on the estimation error, and then the residue generator is constructed to be as sensitive as possible to faults, precisely from this estimation error. It would therefore be interesting to consider alternative structures for the diagnostic modules based on the available input and output signals of the system. Among the possible structures, the use of coprime factorization should be considered for the diagnosis and FTC of nonlinear systems. This technique was used in the linear framework for diagnosis [Frank, 1994]andforFTC [Zhou, 2001], but its extension to the non-linear framework remains open.

To summarize, after a preliminary bibliographical work, the following paths could be explored by the PhD student: - polytopic modelling of transmission faults phenomena, such as saturation and/or dead zones, allowing them to be taken into account in the system model, and may be allowing the estimation of their parameters [Bainier, 2024b, Bezzaoucha, 2016]; - observer-based diagnosis for nonlinear systems based on polytopic / LPV models [Lopez Estrada, 2014, Lopez Estrada, 2019]; - the extension of the Bézier approach proposed by [Bainier, 2024d] to the FTC of TS or LPV systems; - the extension of the coprime factorization-based diagnosis to nonlinear systems represented by polytopic models / LPV; - the extension of the set membership approach for FDI of TS or LPV systems; - the extension of the obtained results to descritor polytopic LPV models [Estrada Manzo, 2015, Lopez Estrada, 2014].