Giacomo Albi, Massimo Fornasier, and Dante Kalise
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 infinite horizon sparse optimal feedback controllers. In order to circumvent the dimensionality issues associated to the control of large-scale agent-based models, we follow a Boltzmann approach. We generate (sub)optimal controls signals for the kinetic limit of the multi-agent dynamics, by sampling of the optimal solution of the associated two-agent dynamics. Numerical experiments assess the performance of the proposed sparse design.
Giacomo Albi, Lorenzo Pareschi
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 computational cost, we introduce a model predictive control (MPC) approximation by deriving a numerical scheme with a feedback selective constrained dynamics. Next, in order to cope with the numerical solution of a large number of interacting agents, we introduce a binary interaction algorithm [http://arxiv.org/abs/1203.0721] which is able to simulate efficiently the selective constrained dynamics. Consistency of the algorithm is also shown in the context of standard kinetic theory. Finally, some numerical simulations are reported to show the efficiency of the proposed techniques.
Giacomo Albi, Mattia Bongini, Emiliano Cristiani, Dante Kalise
In this paper we are concerned with multiscale modeling, control, and simulation of self-organizing agents leaving an unknown area under limited visibility, with special emphasis on crowds. We first introduce a new microscopic model characterized by an exploration phase and an evacuation phase. The main ingredients of the model are an alignment term, accounting for the herding effect typical of uncertain behavior, and a random walk, accounting for the need to explore the environment under limited visibility. We consider both metrical and topological interactions. Moreover, a few special agents, the leaders, not recognized as such by the crowd, are “hidden” in the crowd with a special controlled dynamics. Next, relying on a Boltzmann approach, we derive a mesoscopic model for a continuum density of followers, coupled with a microscopic description for the leaders’ dynamics. Finally, optimal control of the crowd is studied. It is assumed that leaders aim at steering the crowd towards the exits so to ease the evacuation and limit clogging effects, and locally-optimal behavior of leaders is computed. Numerical simulations show the efficiency of the control techniques in both microscopic and mesoscopic settings. We also perform a real experiment with people to study the feasibility of such a bottom-up control technique.
Page with microscopic and mesoscopic simulations.
Article on ‘WIRED.it’.
Giacomo Albi, Lorenzo Pareschi, Mattia Zanella.
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.