1. Boltzmann typecontrol of opinionconsensusMattia ZanellaThe BoltzmannEquationComplexityreductionSHBEMMConstrainedself-organizedsystemsOpinion controlthrough leadersTheBoltzmann-typeoptimal controlFokker-PlanckModelingNumerical resultsTest 1Test 2aTest 2bConclusionsBibliographyBoltzmann type control of opinion consensusMattia ZanellaDepartment of Mathematics and Computer Science,University of Ferrara, ItalyJoint research with:G. Albi (Munich, Germany) L. Pareschi (Ferrara, Italy)XXXIX Summer School on Mathematical PhysicsRavello, September 15-27, 2014Mattia Zanella (University of Ferrara) Boltzmann type control of opinion consensus Ravello September 2014 1 / 26

2. Boltzmann typecontrol of opinionconsensusMattia ZanellaThe BoltzmannEquationComplexityreductionSHBEMMConstrainedself-organizedsystemsOpinion controlthrough leadersTheBoltzmann-typeoptimal controlFokker-PlanckModelingNumerical resultsTest 1Test 2aTest 2bConclusionsBibliographySketch of the presentation1 The Boltzmann EquationComplexity reductionSHBEMM2 Constrained self-organized systemsOpinion control through leadersThe Boltzmann-type optimal control3 Fokker-Planck Modeling4 Numerical resultsTest 1Test 2aTest 2b5 Conclusions6 BibliographyMattia Zanella (University of Ferrara) Boltzmann type control of opinion consensus Ravello September 2014 2 / 26 3. Boltzmann typecontrol of opinionconsensusMattia ZanellaThe BoltzmannEquationComplexityreductionSHBEMMConstrainedself-organizedsystemsOpinion controlthrough leadersTheBoltzmann-typeoptimal controlFokker-PlanckModelingNumerical resultsTest 1Test 2aTest 2bConclusionsBibliographyThe Boltzmann EquationLet us consider DR3 open, limited and regular, and we considerx 2 D and v 2 R3 Then for t 2 [0; T] the Boltzmann Equation is@f(x; v; t)@t+ vrxf(x; v; t) = Q(f; f)f(x; v; 0) = f0(x; v);where we interpret f : DR3[0;+1) ! R+ as a probabilitydensity function and where we de 4. ned the collision operatorQ(f; f)(x; v; t) =ZR3S2[f(x; v; t)f(x;w; t)