Kinetic models are used to describe the behaviour of various physical systems at particle level. Among them, Boltzmann models lead to a very accurate description of the behaviour of the particles. The aim of this talk is a theoretical and numerical investigation of ensemble optimal control problems governed by kinetic models of (multi-species) particle models. The purpose of the control is to drive an ensemble of particles to acquire a desired mean velocity and position and to reach a desired final configuration in phase space. Using an expectation value formulation of the objective and the Lagrange framework for characterizing the optimal control, we derive an adjoint model and reformulate it to interpret it in a kinetic way. We then propose a numerical strategy to solve the arising models using Monte Carlo schemes that are consistent with the kinetic description of gas. As numerical examples, we consider a linear Boltzmann model with the Keilson-Storer collision term and the control mechanism in the external force and a multi-species Vlasov-Poisson plasma with the control assumed to be the external magnetic field.


Contatto: gabriele.ciaramella@polimi.it