Soutenance HDR de D. Liu

Devant le jury constitué par les personnalités suivantes :

• Pierre MELCHIOR Professeur des Universités Bordeaux INP/ENSEIRB-MATMECA
• Mohammed M’SAAD Professeur des Universités ENSI CAEN
• Michel ZASADZINSKI Professeur des Universités IUT Henri Poincaré de LONGWY
• Catherine BONNET Directrice de recherches INRIA Saclay
• Mohamed DJEMA Professeur des Universités Université Polytechnique Hauts-de-France
• Rachid OUTBIB Professeur des Universités Université d’Aix-Marseille
• Gérard POISSON Professeur des Universités IUT Bourges
• Holger VOOS Professeur des Universités Université du Luxembourg
• Driss BOUTAT Professeur des Universités INSA Centre Val de Loire

Résumé des travaux :
In practical applications, due to technical and economic reasons, there are always certain useful parameters and variables that cannot be measured by sensors and need to be estimated from available measurements which usually contain noises. In order to overcome these problems, many estimation methods have been developed. On the one hand, to be precise and reliable, these estimation methods must to be robust against corrupting noises due to physical sensors and \ or poor knowledge of models of real systems. On the other hand, the estimated outcomes generally have to be provided within a finite time, especially for on-line applications responding to real-time control systems. In this context, my research is carried out based on the study of two non-asymptotic and robust estimation methods: the algebraic parametric method and the modulating functions method. Thanks to these methods, the sought parameter and variables can be exactly given by algebraic integral formulas. According to the considered models, my works are divided to four parts. In Part I, the system model of linear differential equation is considered. First, the parameters of fractional order linear systems are estimated. Second, the generalized modulating functions method is introduced for state estimation of integer order linear systems and then it is applied to estimate the non-integer derivatives of the output. Third, the method is applied to estimate the positions and velocities from noisy accelerations. In Part II, the model of pseudo-state space representation is studied for fractional order linear systems. The generalized modulating functions method is applied to estimate the pseudo-state as well as its fractional derivatives by estimating the fractional derivatives of the output and a set of fractional order initial values. In Part III, two fractional order differentiators are introduced without considering any system model, which can be applied to estimate the fractional order derivatives of the output of fractional order nonlinear systems by admitting a time-delay. In Part IV, non-asymptotic state estimation is studied for integer order nonlinear systems using the observer normal forms. First, a family of nonlinear systems is proposed that can be transformed into the output-auxiliary depending observer normal Form by means of a set of changes of coordinates and an auxiliary dynamics. Then, a new modulating functions based state estimation method is introduced based on the nonlinear observer normal form. This new method can be applied to different kinds of systems, such as fractional order nonlinear systems, singular systems and time-delay systems, etc.