Applied Math And Analysis Seminar
Monday, November 13, 2017, 3:00pm, Gross 318
Massimo Fornasier (TU Munich)
Multi-agent system learning and control (mini-course, Mon-Fri)
Abstract:
Course content: This series of informal lectures presents novel results on modeling and control of multi-agent dynamics. We focus in particular on two concepts: - sparse control, i.e., steering a large group of interacting agents by influence parsimoniously only few of them; - mean-field control, i.e., the control of the mean-field equations describing the evolution of the probability distribution of a large population of agents. We conclude the lecture series with some complements related to mean-field games, and the problem of learning the interactions in multi-agent system from the observation of realizations of the dynamics. The lecture series starts with basic results and it requires knowledge of relatively standard functional analysis (mainly basics of metric and Banach spaces and Bochner integration). The analysis content of the lecture series follows: Existence and uniqueness solutions of the Caratheodory differential equations; Classical examples of multiagent dynamics; Wasserstein distances and optimal transport; Existence and uniqueness of mean-field equations; Introduction to optimal control and first order optimality conditions; Introduction to Gamma-convergence; Sparse stabilization and optimal control of multiagent dynamics; Smooth relaxation of sparse mean-field optimal control; Sparse mean-field optimal control; Mean-field Pontryagin maximum principle; Sparse control of alignment models in high dimension; Numerical methods and open problems.

Lecture slides are available here

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