Seminario di equazioni differenziali e applicazioni: “Topics in Analysis and Optimal Control of Multi-Agent Systems”

Lunedì 25 Marzo 2019, ore 12:00 - Sala Riunioni 701 - Benoit Bonnet


Lunedì 25 Marzo 2019 alle ore 12:00 in Sala Riunioni 701, Benoit Bonnet (Université Aix Marseille et Toulon, LIS Marseille) terrà un seminario dal titolo “Topics in Analysis and Optimal Control of Multi-Agent Systems”.

The ever increasing attention devoted to the study of multi-agents systems during the past decades has progressively brought its modelling tools and problems into the realm of control and optimization theory. My aim in this talk will be to describe several problems arising in the community of mean-field control. The aim of the theory of mean-field control is to describe how an external policy maker can act on a large assembly of interacting agents in order to achieve a desired goal, which can be written for instance in the form of an optimization problem. Such an analysis is generally split into two sets of problem. First, identifying interesting global patterns along with the conditions under which they emerge. Then, controlling large assemblies of particles in a savvy way in order to enforce these desired behaviours on general multi-agent systems. Such large finite-dimensional systems are usually out of computational grasp in their discrete form, and are often dealt with through infinite dimensional approximations. In this context, one usually resorts to the well-known mean-field limit method, which allows to trade a large system of ordinary differential equations against a single continuity equation on the density of agents. With these modelling motivations in mind, I will focus on the one hand on the analysis and control of alignment models, which represent a broadly studied topic in multi-agent dynamical systems, and on the other hand on general optimal control problems formulated in the Wasserstein space of probability measures. Connections will be made between the different models involved along with discussions of some further work perspectives on these topics.

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