Section: New Results

Use of geometric techniques for the control of finite and infinite dimensional systems

The paper [31] deals with the design of high gain observers for a class of continuous dynamical systems with discrete-time measurements. The new idea of the this work is to synthesize an observer requiring the less knowledge as possible from the output measurements. This is done by using an updated sampling time observer.

In [12] , it is shown that, for a bilinear system, the property of observability is preserved after sampling provided that the controls take their values in a compact space and do not vary too quickly.

In the note [18] two notions of controllability are studied, called respectively radial controllability and directional controllability. It is proven that for families of linear vector fields, the two notions are actually equivalent.

We used operators theory to obtain some new estimates of the energy of an infinite dimensional bilinear quantum systems. These results were presented in [34] .

Robust control of bilinear Schrödinger equation was investigated in [35] . The use of sharp finite dimensional energy estimates (in the spirit of [34] ) allows to obtain the first approximate ensemble controllability results for infinite dimensional quantum systems, also in presence of mixed spectrum for the free Hamiltonian.

The above energy questions, together with a their relation with some open question in the control of bilinear quantum systems, were gathered in the survey [32] .

Our team is heavily involved in the optimization of driving strategy, and especially in the effective implementation in the prototype build in ESSTIN. MPC related methods have been tested and successfully improved as described in [37] .