Ph. D. Project
Fault diagnosis and fault tolerant control of LPV systems
2021/09/14 - 2024/09/13
Fault diagnosis and fault tolerant control (FTC) are key issues. Indeed, 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) [1]. 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) [3, 9], or
polytopic or TS
systems [12] 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 [6, 13]. 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).

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. According to [11], 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 [2], dead zones, etc).
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 [14]. Several works have already been done in this direction [2], but some obstacles still remain (restrictive assumptions, pessimism of the results, etc.) and limit their
applications. A more accurate description of the saturation phenomena in a polytopic form should make it possible to remove some of these locks.
Constraints on state variables should also be included to take into account the validity domain of the polytopic rewriting of the original nonlinear model [10].
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 [5] and
for FTC [15], but its extension to the non-linear framework remains open.

To summarize, after a preliminary bibliographical work, the following pathes 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
[2] ;
- Observer-based diagnosis for nonlinear systems based on polytopic / LPV models [8, 7] ;
- the extension of the coprime factorization-based diagnosis to nonlinear systems represented by polytopic models / LPV
- the extension of the obtained results to descritor polytopic LPV models [4, 8].

[1] M. Blanke, M. Kinnaert, J. Lunze and M. Staroswiecki, Diagnosis and fault-tolerant control, Springer, 2006.
[2] S. Bezzaoucha, B. Marx, D. Maquin, J. Ragot, State and output feedback control for Takagi-Sugeno systems with saturated actuators, International Journal of Adaptive Control and Signal Processing, 30 : 888-905,
[3] C. Briat, LPV & Time-Delay Systems - Analysis, Observation, Filtering & Control, Springer-Heidelberg, 2015.
[4] V. Estrada Manzo, Estimation et commande des systèmes descripteurs, Thèse de doctorat de l'Université de Valenciennes et du Hainaut-Cambrésis, 2015.
[5] P.M. Frank, X Ding, Frequency Domain Approach to Optimally Robust Residual Generation and Evaluation for Model-based Fault Diagnosis, Automatica, 30(5) : 789-804, 1994.
[6] Z. Lendek, T.M. Guerra, R. Babuska, and B. De Schutter. Stability Analysis and Nonlinear Observer Design using Takagi-Sugeno Fuzzy Models, Springer, 2010.
[7] F.R. Lopez-Estrada, D. Theilliol, C.M. Astorga-Zaragoza, J.C. Ponsart, G. Valencia-Palomo, J.L. Camas-Anzueto, Fault diagnosis observer for descriptor Takagi-Sugeno systems, Neurocomputing, 331 : 10-17, 2019.
[8] F.R. Lopez Estrada, Contribution au diagnostic de défauts à base de modèles : Synthèse d'observateurs pour les systèmes singuliers linéaires à paramètres variants aux fonctions d'ordonnancement non
mesurables, Thèse de doctorat de l'Université de Lorraine, 2014.
[9] B. Marx, D. Ichalal, J. Ragot, D. Maquin, S. Mammar, Unknown input observer for LPV systems, Automatica, 100 : 67-74, 2019.
[10] A.T. Nguyen, A. Dequidt, and M. Dambrine. Anti-windup based dynamic output feedback controller design with performance consideration for constrained Takagi-Sugeno systems. Engineering Applications of
Artificial Intelligence, 40 : 76-83, 2015.
[11] F. Pasqualetti, F. Dorfler, F. Bullo, Attack Detection and Identification in Cyber-Physical Systems, IEEE Transactions on Automatic Control, 58(11) : 2715-2729, 2013.
[12] T. Takagi and M. Sugeno. Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man and Cybernetics, 15(1) :116-132, 1985.
[13] K. Tanaka and H.O. Wang. Fuzzy Control Systems Design and Analysis : A Linear Matrix Inequality Approach. Wiley, 2001.
[14] S. Tarbouriech, G. Garcia, J.M. Gomes da Silva, Jr., and I. Queinnec. Stability and Stabilization of Linear Systems with Saturating Actuators. Springer, 2011.
[15] K. Zhou and Z. Ren. A new controller architecture for high performance, robust, and fault-tolerant control. IEEE Transactions on Automatic Control, 46(10) :1613-1618, 2001.
Control Identification Diagnosis