Pontryagin's Maximum Principle and Mean Field optimality conditions for interacting agent systems

Venue: Seminar Room “-1” – Department of Mathematics – Via Sommarive, 14 Povo - Trento
Time: 15.00 p.m.

• Chiara Segala - PhD in Mathematics

Abstract:
We state and prove the Pontryagin's Maximum Principle and we derive optimality conditions for controlled interacting agent systems.
In the case of finitely many interacting agents the associated control problem can be solved using the PMP, then we are interested in the mean field of the optimality conditions arising from the PMP and its relation to the multipliers obtained by the optimization with respect to the partial differential equation.
The link is important for many recently published articles on control strategies for agents.

References:
- A. Bressan lecture notes: Viscosity solutions of Hamilton-Jacobi Equations and Optimal Control Problems, 2011.
- M. Herty and C. Ringhofer: Consistent mean field optimality conditions for interacting agent systems, preprint, 2019.
- A. Marigonda lecture notes: Optimization, 2018

The seminar is part of the examination of the course “Mean Field Games and Optimal Transport”

Supervisor: Fabio Bagagiolo