Doctorant sous la direction de

**A. Loria****Titre de la thèse:**Observation problems in regenerative braking of electric vehicles during ABS activation

**Résumé de la thèse:**In the context of vehicle and motor control, the observation of non-uniformly observable systems is a recurrent problem. It appears, for example, when trying to estimate the velocity of the vehicle Corno-Panzani-Savaresi (2013) or the extended braking stiffness of tires Hoang et al. (2014b). In the particular case of electric vehicles, it appears additionally in several questions related to electric motor control, where several state variables are observable only if the currents applied to the system satisfy some conditions. In the last few years, the observation problem has been considered for several classes of non-uniformly observable systems. For example, for systems that are affine (with respect to the unmeasured states) up to a multiplication by a function of the output, the approach proposed by Respondek-Pogromsky-Nijmeijer (2004), has been extended by Hoang et al. (2014a) to cover the case of singular time rescalings (and thus to deal with a class of non-uniformly observable systems). In that work the observer problem is solved by transforming the observer error dynamics into a switched linear system, for which several stability analysis methods are available. In particular, the Lasalle-like approach of Hespanha (2004) can be used directly to prove the stability of the constructed observer. Another example is the observation problem for the synchronization of chaotic systems; in Loría-Panteley-Zavala (2009), they use the concept of persistency of excitation to design an observer by establishing a property of uniform detectability, which is a weaker condition than uniform observability. Even if, at a first glance, the techniques used in those works seem completely different, they share several common points that might indicate that the two considered classes belong to a more general category of non-uniformly observable systems, for which an observer can be constructed. The aim of this Ph.D. thesis is thus to explore new methodological ideas in order to solve the observation problem for new classes of non-uniformly observable nonlinear systems and, at the same time, to validate these new ideas on concrete observation problems coming from the area of vehicle control. Ideally, this validation should be done on experimental data. In this context, the experimental setup that has been constructed by the LTN during the last four years will be a key component to test the results of this study.