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Mean-field sparse optimal control.

Massimo Fornasier1, Benedetto Piccoli2, Francesco Rossi3

  • 1Technische Universität München, Fakultät Mathematik, Boltzmannstrasse 3 85748, Garching bei München, Germany massimo.fornasier@ma.tum.de.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|October 8, 2014
PubMed
Summary
This summary is machine-generated.

This study develops sparse optimal control for large populations, linking finite to infinite dimensions. It models interventions on leader-follower dynamics, influenced by external policies, as population size grows.

Keywords:
mean-field limitoptimal control with ODE–PDE constraintssparse optimal controlΓ-limit

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Area of Science:

  • Control Theory
  • Mathematical Modeling
  • Population Dynamics

Background:

  • Classical mean-field theory simplifies interactions in large populations.
  • Existing models often lack external policy influence on population dynamics.

Purpose of the Study:

  • To develop a rigorous limit process for sparse optimal control problems.
  • To model parsimonious interventions in leader-follower population dynamics.
  • To analyze the influence of external policies on large populations.

Main Methods:

  • Connecting finite-dimensional optimal control problems with ODE constraints to infinite-dimensional problems.
  • Utilizing a Vlasov-type PDE for follower distribution dynamics.
  • Employing simultaneous mean-field limit and Gamma-limit derivations.

Main Results:

  • Established a rigorous connection between finite and infinite-dimensional sparse optimal control.
  • Modeled population dynamics with external policy influence and leader-follower structures.
  • Propagated policy effects as the follower population approaches infinity.

Conclusions:

  • The study provides a novel framework for sparse mean-field optimal control.
  • The methods are applicable to systems with external policy interventions.
  • This work extends mean-field theory to include directed influence.