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Seminar
FIELD Mathematics
DATE February 17 (Wed), 2021
TIME 16:00-17:00
PLACE Online
SPEAKER 고동남
HOST Kim, Doheon
INSTITUTE 가톨릭대학교
TITLE Dynamics and control for multi-agent networked systems: a finite difference approach
ABSTRACT We analyze the dynamics of multi-agent collective behavior models and their control theoretical properties. We first derive a large population limit to parabolic diffusive equations and then address the control problem in the linear setting, linking the multi-agent model with the spatial semi-discretization of parabolic equations. This allows us to use the existing techniques for parabolic control problems in the present setting and derive explicit estimates on the cost of controlling these systems as the number of agents tends to infinity. Our approach, inspired on the existing results for parabolic equations, possibly of fractional type, and in several space dimensions, shows that the formation of consensus may be understood in terms of the underlying diffusion process described by the heat semi-group.
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