Author Archives: giacomoalbi

Linear multistep methods for optimal control problems and applications to hyperbolic relaxation systems

with Michael Herty, Lorenzo Pareschi (23/07/2018, arxiv.1807.08547) We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of accuracy … Continue reading

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Pressureless Euler alignment system with control

Giacomo Albi, Young-Pil Choi, Axel-Stefan Haeck (31/01/2018,  arxiv:1801.10587) We study a non-local hydrodynamic system with control. First we characterize the control dynamics as a sub-optimal approximation to the optimal control problem constrained to the evolution of the pressureless Euler alignment system. We then … Continue reading

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Boltzmann games in heterogeneous consensus dynamics

Giacomo Albi, Lorenzo Pareschi, Mattia Zanella (07/12/17,  arxiv:1712.03224) We consider a constrained hierarchical opinion dynamics in the case of leaders’ competition and with complete information among leaders. Each leaders’ group tries to drive the followers’ opinion towards a desired state accordingly … Continue reading

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A Boltzmann approach to mean-field sparse feedback control

Giacomo Albi, Massimo Fornasier, and Dante Kalise (12/11/2016 arxiv.org/abs/1611.03988) We study the synthesis of optimal control policies for large-scale multi-agent systems. The optimal control design induces a parsimonious control intervention by means of l-1, sparsity-promoting control penalizations. We study instantaneous and … Continue reading

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Mean field control hierarchy

Giacomo Albi, Young-Pil Choi, Massimo Fornasier, and Dante Kalise (01/08/2016  arxiv.org/abs/1608.01728) In this paper we model the role of a government of a large population as a mean field optimal control problem. Such control problems are constrainted by a PDE … Continue reading

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Recent advances in opinion modeling: control and social influence

Giacomo Albi, Lorenzo Pareschi, Giuseppe Toscani, Mattia Zanella (01/07/2016, arxiv.org/abs/1607.05853 to appear in  springer.com/series/4960) 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 … Continue reading

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Discrete and Continuum Modeling of Biological Network Formation

Giacomo Albi, Martin Burger, Jan Haskovec, Peter Markowich and Matthias Schlottbom (01/06/2016  to appear in  springer.com/series/4960 ) We present an overview of recent analytical and numerical results for the elliptic parabolic system of partial differential equations proposed by Hu and Cai, … Continue reading

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Opinion dynamics over complex networks: kinetic modeling and numerical methods

Giacomo Albi, Lorenzo Pareschi, Mattia Zanella (31/03/2016 arxiv.org/abs/1604.00421) In this paper we consider the modeling of opinion dynamics over time dependent large scale networks. A kinetic description of the agents’ distribution over the evolving network is considered which combines an opinion … Continue reading

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Selective model-predictive control for flocking systems

Giacomo Albi, Lorenzo Pareschi (16/03/2016 arxiv.org/abs/1603.05012) In this paper the optimal control of alignment models composed by a large number of agents is investigated in presence of a selective action of the control. As a first step toward a reduction of … Continue reading

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