Search results for " adversarial disturbance"

showing 3 items of 3 documents

Crowd-Averse Robust Mean-Field Games: Approximation via State Space Extension

2016

We consider a population of dynamic agents, also referred to as players. The state of each player evolves according to a linear stochastic differential equation driven by a Brownian motion and under the influence of a control and an adversarial disturbance. Every player minimizes a cost functional which involves quadratic terms on state and control plus a cross-coupling mean-field term measuring the congestion resulting from the collective behavior, which motivates the term “crowd-averse.” Motivations for this model are analyzed and discussed in three main contexts: a stock market application, a production engineering example, and a dynamic demand management problem in power systems. For th…

0209 industrial biotechnologyStochastic stabilityMathematical optimizationCollective behaviorTechnologyComputer sciencePopulationcontrol designcrowd-averse robust mean-field games state space extension dynamic agents linear stochastic differential equation Brownian motion adversarial disturbance cost functional cross-coupling mean-field term collective behavior stock market application production engineering example dynamic demand management problem robust mean-field game approximation error stochastic stability microscopic dynamics macroscopic dynamicscontrol engineering02 engineering and technology01 natural sciencesStochastic differential equationoptimal control020901 industrial engineering & automationQuadratic equationAutomation & Control SystemsEngineeringClosed loop systemsSettore ING-INF/04 - AutomaticaApproximation errorRobustness (computer science)Control theory0102 Applied MathematicsState space0101 mathematicsElectrical and Electronic EngineeringeducationBrownian motioneducation.field_of_studyScience & TechnologyStochastic process010102 general mathematicsRelaxation (iterative method)Engineering Electrical & ElectronicOptimal controlComputer Science Applications0906 Electrical and Electronic EngineeringIndustrial Engineering & AutomationMean field theoryControl and Systems EngineeringSettore MAT/09 - Ricerca Operativa0913 Mechanical Engineering
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Crowd-Averse Cyber-Physical Systems: The Paradigm of Robust Mean-Field Games

2016

For a networked controlled system, we illustrate the paradigm of robust mean-field games. This is a modeling framework at the interface of differential game theory, mathematical physics, and $H_{\infty}$ - optimal control that tries to capture the mutual influence between a crowd and its individuals. First, we establish a mean-field system for such games including the effects of adversarial disturbances. Second, we identify the optimal response of the individuals for a given population behavior. Third, we provide an analysis of equilibria and their stability.

Computer Science::Computer Science and Game Theory0209 industrial biotechnologyTheoretical computer scienceComputer scienceInterface (computing)PopulationStability (learning theory)02 engineering and technology01 natural sciencesAdversarial system020901 industrial engineering & automationSettore ING-INF/04 - AutomaticaControl theoryRobustness (computer science)Differential game0101 mathematicsElectrical and Electronic Engineeringcrowd-averse cyber-physical systems robust mean-field games paradigm networked control system differential game theory mathematical physics H∞-optimal control mean-field system adversarial disturbance effecteducationeducation.field_of_studyCyber-physical systemOptimal controlComputer Science Applications010101 applied mathematicsControl and Systems EngineeringSettore MAT/09 - Ricerca OperativaIEEE Transactions on Automatic Control
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Distributed $n$-player approachability and consensus in coalitional games

2015

We study a distributed allocation process where, at each time, every player: i) proposes a new bid based on the average utilities produced up to that time, ii) adjusts such allocations based on the inputs received from its neighbors, and iii) generates and allocates new utilities. The average allocations evolve according to a doubly (over time and space) averaging algorithm. We study conditions under which the average allocations reach consensus to any point within a predefined target set even in the presence of adversarial disturbances. Motivations arise in the context of coalitional games with transferable utilities (TU) where the target set is any set of allocations that makes the grand …

game theorydistributed control consensus game theory coalitional gamesdistributed controldistributed n-player approachability distributed n-player consensus coalitional games distributed allocation process utility allocation doubly averaging algorithm adversarial disturbance transferable utilities grand coalition stabilityOptimization and Control (math.OC)consensuFOS: MathematicsSettore MAT/09 - Ricerca OperativaMathematics - Optimization and Controlcoalitional games
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