| Abstract: |
| We present a Boltzmann-type framework to deal with the optimal control of large particle systems.
We will propose two main approaches, the first one based on the construction of a control hierarchy at level of the binary interactions, the second one which tackle directly the optimal control of the Boltzmann equation.
In particular, we construct a control hierarchy for a finite time horizon. We will show that, under a suitable scaling limit, this class of problems converges towards corresponding mean-field optimal control problems.
A set of stochastic particle approximations is derived, coupling Monte-Carlo methods with model predictive control, and dynamic programming.
This novel approach permits to tackle the curse of dimensionality, and to perform efficient numerical simulations. Several examples from consensus dynamics to swarming models are presented.
This is a joint work with Y-P. Choi, M. Fornasier, D. Kalise, and with L. Pareschi. |
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