# Massimo Fornasier : Sparse Stabilization and Optimal Control in Consensus Emergence

From a mathematical point of view self-organization can be described as the formation of patterns, where certain dynamical systems modeling social dynamics tend autonomously to converge. The fascinating mechanism to be revealed by such a modeling is how to connect the microscopical and usually binary rules or social forces of interaction between individuals with the eventual global behavior or group pattern, forming as a superposition in time of the different microscopical effects. In this talk we explore mechanisms to go beyond self-organization, in particular how to externally control such dynamical systems in order to eventually enforce pattern formation also in those situations where this wished phenomenon does not result from spontaneous and autonomous convergence. Our focus is on dynamical systems of Cucker-Smale type, modeling consensus emergence, and we question the existence of stabilization and optimal control strategies which require the minimal amount of external intervention for nevertheless inducing consensus in a group of interacting agents. On the one hand and formally, our main result realizes the connection between certain variational problems involving L1-norm terms and optimal sparse controls. On the other hand, our findings can be informally stated in terms of the general principle for which "A policy maker should always consider more favorable to intervene with stronger actions on the fewest possible instantaneous optimal leaders than trying to control more agents, with minor strength".

**Category**: Applied Math and Analysis**Duration**: 01:23:18**Date**: October 9, 2012 at 4:25 PM**Views**: 101-
**Tags:**seminar, Applied Math And Analysis Seminar

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