Performance bounds for the mean-field limit of constrained dynamics

performance_boundplotMichael 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.

On the optimal control of opinion dynamics on evolving networks

 

immagine_sitoGiacomo Albi, Lorenzo Pareschi, Mattia Zanella 

System Modeling and Optimization, 27th IFIP TC7 Conference, CSMO 2015, Sophia Antipolis, France, June 29-July 3, 2015. 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.

Uncertainty Quantification in Control Problems for Flocking Models

Giacomo Albi, Lorenzo Pareschi, Mattia Zanella

Mathematical Problems in Engineering, Vol. 2015. Open Access. 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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Form and Urban Change. An urban morphology study of five gentrified neighbourhoods in London

baAlessandro Venerandi, Mattia Zanella, Ombretta Romice, Sergio Porta (To appear in Environment and Planning B)              

Many socioeconomic studies have been carried out to explain the phenomenon of gentrification. Although results of these works shed light on the process around this phenomenon, a perspective which focuses on the relationship between city form and gentrification is still missing. With this paper we try to address this gap by studying and comparing, through classic methods of mathematical statistics, morphological features of five London gentrified neighbourhoods. Outcomes confirm that areas which have undergone gentrification display similar and recognizable morphological patterns in terms of urban type and geographical location of main and local roads as well as businesses. These initial results confirm findings from previous research in urban sociology, and highlight the role of urban form in contributing to shape dynamics of non-spatial nature in cities.

Philip Ball’s comment on The Guardian: Logo-GuardianGentrification is a natural evolution | Philip Ball | Comment is free | theguardian.com

 

 

 

Stochastic modeling and simulation of ion transport through channels

Fig6d_grandeDaniela Morale, Mattia Zanella, Vincenzo Capasso, Willi Jäger                                                                                            

SIAM Journal on Multiscale Modeling & Simulation, vol. 14(1): 113-137. Preprint arXiv.

Ion channels are of major interest and form an area of intensive
research in the fields of biophysics and medicine since they control many vital physiological functions. The aim of this work is on one hand to propose a fully stochastic and discrete model describing the main characteristics of a multiple channel system. The movement of the ions is coupled, as usual, with a Poisson equation for the electrical field; we have considered, in addition, the influence of exclusion forces. On the other hand, we have discussed about the nondimensionalization of the stochastic system by using real physical parameters, all supported by numerical simulations. The specific features of both cases of micro- and nanochannels have been taken in due consideration with particular attention to the latter case in order to show that it is necessary to consider a discrete and stochastic model for ions movement inside the channels.

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Boltzmann-type control of opinion consensus through leaders

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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