Approches fondées sur des modèles énergétiques pour l'analyse formelle et la commande des systèmes non linéaires hybrides

摘要

The research works described in the dissertation deal with modelling, analysis and control of dynamical systems with heterogeneous features, using knowledge model-based approaches. Despite a wide variety of objects, there are characterized by a methodological unity due to the genericity of these approaches. The modelling aspects are essentially based on the choice of the bond graph, which allows physical heterogeneity to be managed in a unified manner through the energy point of view. The bond graph is first used as a modelling tool stricto sensu, in various fields including mechatronics, cardiovascular physiology and power electronics (static converters). The main contribution of the corresponding works has consisted of enlarging the validity domain of bond graph approach to new classes of complex systems, searching for sytematical model synthesis strategies in each case. Tree specific forms of complexity have been considered, with a common hybrid character which can either refer to the coupling between several physical fields (multidisciplinary systems), or between lumped and distributed parameters (spatial hybridism), or eventually between time-continuous and discrete-event dynamics (time hybridism, switching systems). In the logical continuation of the previous activities, a large part of our works focuses on formal analysis of bond graph models, with the extension of existing methodologies and the development of new original ones. The first class of methodologies studied aims at supplying bond graph models with other complementary kinds of dynamicals representations such as state space models or transfer functions, one of the important stakes being the explicitation of models initially expressed in an implicit way, so as to make their simulation by standard solvers possible. Another class of analysis methods relates to the direct exploitation of bond graph models, in order to display some structural properties such as differential flatness. Within these works concerning formal analysis, a special emphasis is put on switching systems, which correspond to one of the main theoretical themes of ASH research team. The third and last part of the research activities presented in the dissertation is devoted to control. Altough it also comes as a natural continuation of both previous ones, it is tackled from another angle, which does not directly relates to bond graph any longer. The corresponding theoretical studies are essentially based on the nonlinear concept of sliding mode. Sliding mode control, which is a widely used principle in many engineering applications, is specifically considered here in the context of dynamical systems with logical control inputs (including switching systems). New binary sliding mode control strategies are developped, which can be straightforwardly applied to such systems, without requiring any additional PWM.