Andrea Tosin, Mattia Zanella.
IFAC-PapersOnLine, 51(9): 67-72, 2018. (Preprint arXiv)
In this paper we present a Boltzmann-type kinetic approach to the modelling of road traffic, which includes control strategies at the level of microscopic binary interactions aimed at the mitigation of speed-dependent road risk factors. Such a description is meant to mimic a system of driver-assist vehicles, which by responding locally to the actions of their drivers can impact on the large-scale traffic dynamics, including those related to the collective road risk and safety.
Giacomo Albi, Lorenzo Pareschi, Giuseppe Toscani, Mattia Zanella
Active Particles, Volulme 1. Advances in Theory, Models, and Applications, pp. 49-98, 2017. (Preprint arXiv)
We survey some recent developments on the mathematical modeling of opinion dynamics. After an introduction on opinion modeling through interacting multi-agent systems described by partial differential equations of kinetic type, we focus our attention on two major advancements: optimal control of opinion formation and influence of additional social aspects, like conviction and number of connections in social networks, which modify the agents’ role in the opinion exchange process.
Michael Herty, Mattia Zanella
Discrete and Continuous Dynamical Systems – Series A, 37(4): 2023-2043, 2017. (Preprint arXiv)
In this work we are interested in the mean-field formulation of kinetic models under control actions where the control is formulated through a model predictive control strategy (MPC) with varying horizon. The relation between the (usually hard to compute) optimal control and the MPC approach is investigated theoretically in the mean-field limit. We establish a computable and provable bound on the difference in the cost functional for MPC controlled and optimal controlled system dynamics in the mean-field limit. The result of the present work extends previous findings for systems of ordinary differential equations. Numerical results in the mean-field setting are given.
G. Albi, L. Pareschi, M. Zanella
System Modeling and Optimization. CSMO 2015. IFIP Advances in Information and Communication Technology, vol 494, 2016. (Preprint arXiv)
In this work we are interested in the modelling and control of opinion dynamics spreading on a time evolving network with scale-free asymptotic degree distribution. The mathematical model is formulated as a coupling of an opinion alignment system with a probabilistic description of the network. The optimal control problem aims at forcing consensus over the network, to this goal a control strategy based on the degree of connection of each agent has been designed. A numerical method based on a model predictive strategy is then developed and different numerical tests are reported. The results show that in this way it is possible to drive the overall opinion toward a desired state even if we control only a suitable fraction of the nodes.
Giacomo Albi, Lorenzo Pareschi, Mattia Zanella
Mathematical Problems in Engineering, Vol. 2015, 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.
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.
Article on the Italian blog Gli Stati Generali: Manuale per un leader: strategie matematiche di controllo dell’opinione pubblica.