Exploitable results Control theory and applications The research activities have been covering the following fields: 1. Linear waves. It turns out that at high frequency linear waves propagate according to the law of geometric optic and this has been the guideline of our common work. This is an old idea which goes back probably to Huyghens. However, owing to the Heisenberg principle which prevents localisation both in space and in velocity, the mathematical formalisation is not easy and has been the object of the activities of several generations of pure or applied mathematicians. The recent introduction of the defect measures (which measure the local propagation of energy) make it possible to obtain qualitative information and precise relations for numerical simulations for the inverse problem. Such numerical simulations have been finalised. In fact since the realisation of numerical codes is really time consuming the extension was really instrumental for this phase of the project. 2. Control of Dynamical Systems. Optimal control leads to process which may be discontinuous (the bang-bang control) and therefore the structure of the minimal geodesic is complex and it is important to understand this structure. This leads to the notion of sub-Riemannian geometry. In this field important progress has been made. The results being systematic interpretation of problems arising in the control theory for non-linear ordinary differential equations. In the mean time, it has been considered the question of the local in time approximations of high order for control systems: Find (given the description of the initial trajectory) what perturbation should be used to deviate from this trajectory in a given direction. Such questions may be of importance for satellite guidance. Finally some direct results on the stabilisation of homogenous system were obtained. 3. Fluid dynamic. It has been proven that the system of the incompressible Euler equations is exactly controllable. This turns out to be important for the design of active surfaces in aerodynamic. The method itself is also important because by its local linearisation it gives an algorithm that will help the design of real devices. Searching for OpenAIRE data... There was an error trying to search data from OpenAIRE No results available
