The COMEDY team is interested in the analysis of structural properties and control of classes of dynamical systems such as nonlinear, hybrid, quantum and systems described by partial differential equations. The main focus is on fundamental results, but with a strong link to applications.
Among the fields of application we recall:
Hybrid and switching systems involve both continuous and discrete (event) dynamics. The analysis and control of these systems require dedicated tools. The topics of interest of the team mainly concern the stability properties of deterministic or stochastic switching systems, symbolic control for continuous or hybrid dynamical systems, the analysis of timing contracts, as well as sampled systems.
Partial differential equations describe a wide spectrum of physical systems of infinite dimension. The team employs several methods to analyse and control such systems, from the notion of flatness to singular perturbations, from geometric approaches to Lyapunov methods. More specific methods are also being developed for estimation, filtering and control problems of quantum systems.
The control of mechanical systems, in particular under-actuated and uncertain systems, is addressed with Lyapunov-type or passivity-based approaches, while the trajectory generation and tracking, with or without constraints, is dealt with methods based on differential flatness. In addition, methods based on the input-to-state stability formalism prove to be very useful for studying the robustness of interconnected systems. The geometric methods studied by the team are also of interest both from a theoretical (structural properties of holonomic systems) and an applicative (reconstruction of neuro-inspired images) point of view.