Category Archives: Optimization and Control

Uncertainty Quantification in Control Problems for Flocking Models

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Giacomo Albi, Lorenzo Pareschi, Mattia Zanella

Mathematical Problems in Engineering, Vol. 2015.  (Preprint arXiv)

In this paper the optimal control of flocking models with random inputs is investigated from a numerical point of view. The effect of uncertainty in the interaction parameters is studied for a Cucker-Smale type model using a generalized polynomial chaos (gPC) approach. Numerical evidence of threshold effects in the alignment dynamic due to the random parameters is given. The use of a selective model predictive control permits to steer the system towards the desired state even in unstable regimes.

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Boltzmann-type control of opinion consensus through leaders

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Kinetic_density_leaders_12 Giacomo Albi, Lorenzo Pareschi, Mattia Zanella    

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Science, 2014 372 20140138. (Preprint arXiv)

The study of formations and dynamics of opinions leading to the so called opinion consensus is one of the most important areas in mathematical modeling of social sciences. Following the Boltzmann type control recently introduced in [G. Albi, M. Herty, L. Pareschi arXiv:1401.7798], we consider a group of opinion leaders which modify their strategy accordingly to an objective functional with the aim to achieve opinion consensus. The main feature of the Boltzmann type control is that, thanks to an instantaneous binary control formulation, it permits to embed the minimization of the cost functional into the microscopic leaders interactions of the corresponding Boltzmann equation. The related Fokker-Planck asymptotic limits are also derived which allow to give explicit expressions of stationary solutions. The results demonstrate the validity of the Boltzmann type control approach and the capability of the leaders control to strategically lead the followers opinion.

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Article on the Italian blog Gli Stati Generali: Manuale per un leader: strategie matematiche di controllo dell’opinione pubblica.

 

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