Confinement Strategies in a Model for the Interaction between Individuals and a Continuum

Colombo, Rinaldo M.; Pogodaev, Nikolay

doi:10.1137/110854321

Cited by 25 publications

(18 citation statements)

References 16 publications

(32 reference statements)

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“…Control mechanisms of self-organized systems have been studied for macroscopic models in [12,13] and for kinetic and hydrodynamic models in [2,20,30]. However, in the above references, the control is modeled as a leader dynamics.…”

Section: Introductionmentioning

confidence: 99%

Kinetic description of optimal control problems and applications to opinion consensus

Albi

Herty

Pareschi

2015

Communications in Mathematical Sciences

100

168

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In this paper an optimal control problem for a large system of interacting agents is considered using a kinetic perspective. As a prototype model we analyze a microscopic model of opinion formation under constraints. For this problem a Boltzmann-type equation based on a model predictive control formulation is introduced and discussed. In particular, the receding horizon strategy permits to embed the minimization of suitable cost functional into binary particle interactions. The corresponding Fokker-Planck asymptotic limit is also derived and explicit expressions of stationary solutions are given. Several numerical results showing the robustness of the present approach are finally reported

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Section: Introductionmentioning

confidence: 99%

Kinetic description of optimal control problems and applications to opinion consensus

Albi

Herty

Pareschi

2015

Communications in Mathematical Sciences

100

168

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“…Opinion dynamics in the presence of different populations has been previously been introduced in [24][25][26]. We mention here that control through leaders in self-organized flocking systems has been studied in [6,8,27].…”

Section: Introductionmentioning

confidence: 99%

Boltzmann-type control of opinion consensus through leaders

Albi

Pareschi

Zanella

2014

Phil. Trans. R. Soc. A.

114

159

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The study of formations and dynamics of opinions leading to the so-called opinion consensus is one of the most important areas in mathematical modelling of social sciences. Following the Boltzmann-type control approach recently introduced by the first two authors, we consider a group of opinion leaders who modify their strategy accordingly to an objective functional with the aim of achieving opinion consensus. The main feature of the Boltzmann-type control is that, owing to an instantaneous binary control formulation, it permits the minimization of the cost functional to be embedded into the microscopic leaders’ interactions of the corresponding Boltzmann equation. The related Fokker–Planck asymptotic limits are also derived, which allow one 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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“…ADR PDEs have also been used to control the probability density functions (pdfs) of multidimensional stochastic processes [2], develop multiagent coverage and search strategies that are inspired by bacterial chemotaxis [22], and maximize the probability of swarm robotic presence in a desired region [23]. Other work on PDE-based analysis and design of agent control laws includes a study of multiagent consensus protocols in an Eulerian framework [8]; strategies for confining a population of agents, represented as a continuum, with a few discrete leader agents [10]; and an approach to flocking control for a group of agents governed by the kinetic Cucker-Smale model [26].…”

Section: Performance Bounds On Spatial Coveragementioning

confidence: 99%

Performance Bounds on Spatial Coverage Tasks by Stochastic Robotic Swarms

Zhang

Bertozzi

Elamvazhuthi

et al. 2018

IEEE Trans. Automat. Contr.

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Abstract-This paper presents a novel procedure for computing parameters of a robotic swarm that guarantee coverage performance by the swarm within a specified error from a target spatial distribution. The main contribution of this paper is the analysis of the dependence of this error on two key parameters: the number of robots in the swarm and the robot sensing radius. The robots cannot localize or communicate with one another, and they exhibit stochasticity in their motion and task-switching policies. We model the population dynamics of the swarm as an advectiondiffusion-reaction partial differential equation (PDE) with time-dependent advection and reaction terms. We derive rigorous bounds on the discrepancies between the target distribution and the coverage achieved by individual-based and PDE models of the swarm. We use these bounds to select the swarm size that will achieve coverage performance within a given error and the corresponding robot sensing radius that will minimize this error. We also apply the optimal control approach from our prior work in [13] to compute the robots' velocity field and task-switching rates. We validate our procedure through simulations of a scenario, in which a robotic swarm must achieve a specified density of pollination activity over a crop field.

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Confinement Strategies in a Model for the Interaction between Individuals and a Continuum

Cited by 25 publications

References 16 publications

Kinetic description of optimal control problems and applications to opinion consensus

Kinetic description of optimal control problems and applications to opinion consensus

Boltzmann-type control of opinion consensus through leaders

Performance Bounds on Spatial Coverage Tasks by Stochastic Robotic Swarms

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