Multi-scale modeling and control of self-organized systems: kinetic approximation and numerical methods

Supervisor
Giacomo Albi - Technische Universit√§t M√ľnchen
Date and time
Tuesday, April 26, 2016 at 5:00 PM - Sala verde - Rinfresco 16.45, inizio seminario 17.00
Place
Ca' Vignal - Piramide, Floor 0, Hall Verde
Programme Director
External reference
Marco Caliari
Publication date
April 15, 2016
Department
Computer Science  

Summary

In the first part of this talk I will briefly discuss the multi-scale modeling of self-organized systems, with regard to application in social phenomena like swarming, opinion and crowds dynamics. In this context, I will introduce a class of optimal control problems, in order to promote the emergence of a desired state, through centralized or sparse strategies. Due to the presence of a large number of interacting agents, the numerical treatment of this type of problems is in general affected by the curse of high-dimensionality. Therefore I will propose a stochastic method based on the binary approximation of the microscopic dynamics, which will reduce considerably the computational cost. The consistency of this numerical approach is provided in the context of standard kinetic theory, and it is based on the grazing collision limit of the Boltzmann-Povzner equation. Several simulations and numerical examples will show the efficiency of the method for the constrained dynamics.

Keywords: Multi-agent systems, optimal control, Boltzmann equation, Vlasov dynamics, Direct Simulation Monte-Carlo methods.

 www-m15.ma.tum.de/Allgemeines/GiacomoAlbi

 






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