Orateur
Description
I will first recall some results on how to achieve consensus for well known classes of systems, like the celebrated Cucker-Smale or Hegselmann-Krause models. When the systems are symmetric, convergence to consensus is classically established by proving, for instance, that the usual variance is an exponentially decreasing Lyapunov function: this is a "L^2 theory". When the systems are not symmetric, no L^2 theory existed until now and convergence was proved by means of a "L^\infty theory".
In this talk I will show how to develop a L^2 theory by designing an adequately weighted variance, and how to obtain the sharp rate of exponential convergence to consensus for general finite and infinite-dimensional linear first-order consensus systems.
If time allows, I will show applications in which one is interested in controlling vote behaviors in an opinion model. This is a work in collaboration with Laurent Boudin and Francesco Salvarani.
