## Research domain

The main research topic of GECO is geometric control, with a special focus on control
design and on applications to quantum systems, neurophysiology and switched systems.

Geometric control theory provides a general framework, based on methods issuing from differential geometry,
to tackle questions arising in the control framework: controllability, observability,
stabilization, optimal control... The geometric control approach is particularly well suited for
systems characterized by nonlinear and nonholonomic phenomena.
GECO tackles, from a common geometric viewpoint, control systems of both finite and infinite
dimension.

### Quantum control

The first application domain of GECO is quantum control. The goal is to control the evolution of a system described by the laws of quantum mechanics using one or several external fields (magnetic or electric fields).
Quantum control plays an important role in several domains, including photochemistry (control by laser pulses of chemical reactions), nuclear magnetic resonance (NMR, control by a magnetic field of spin dynamics) and, on a more distant time horizon, quantum computing. NMR is one of the most promising platforms for the implementation of quantum computers. The rapid evolution of these domains is driven by a multitude of
experiments getting more and more precise and complex.
Control techniques should necessarily be innovative, in order to take into account the physical peculiarities of the model and the specific experimental constraints. Our goal is to contribute to the understanding of these control problems and to prose adapted control algorithms.

### Neurophysiology

A second application area concerns problems issuing from neurophysiology. We deal in particular with the modeling of the mechanisms supervising some biomechanics actions or sensorial reactions such as, for instance, eyes movement, body motion and image reconstruction by the primary visual cortex. All these phenomena can be interpreted as control tasks carried out by the brain.

### Switched systems

As a third applicative domain is that of switched systems. The goal is to analyze and control the dynamical behavior of families of control systems of the same type. Switched systems provide a popular modeling framework for heterogeneous aspects issuing from automotive and transportation industry, energy management and factory automation. Our approach to switched systems combines classical matrix algebra techniques with a geometric focus on collective dynamics.