"Random Lift Of Set-Valued Maps And Applications" - Rossana Capuani
Abstract: We discuss some preliminary results about the lifting of set-valued maps defined between Polish spaces to set-valued maps defined between the corresponding spaces of probability measures. In particular, we are interested to establish conditions granting that some relevant properties (for instance semicontinuity, compactness of the images, Lipschitz continuity,...) of the original set-valued maps are conserved also in the lifted map.
The main motivation of the study is the dynamics and the control of multi-agent systems, where the macroscopical trajectory can be seen as the lift of the solution set-valued map of a differential inclusion expressing the microscopical dynamics of the agent, however our results can be extended to more general set-valued maps of agent trajectories provided that they enjoys some properties.
These results have been obtained in collaboration with Antonio Marigonda (University of Verona) and Michele Ricciardi (University of Verona).
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