Search results for "Dynamic demand management"

showing 2 items of 2 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
researchProduct

Mean-field games and dynamic demand management in power grids

2013

This paper applies mean-field game theory to dynamic demand management. For a large population of electrical heating or cooling appliances (called agents), we provide a mean-field game that guarantees desynchronization of the agents thus improving the power network resilience. Second, for the game at hand, we exhibit a mean-field equilibrium, where each agent adopts a bang-bang switching control with threshold placed at a nominal temperature. At equilibrium, through an opportune design of the terminal penalty, the switching control regulates the mean temperature (computed over the population) and the mains frequency around the nominal value. To overcome Zeno phenomena we also adjust the ban…

Statistics and ProbabilityEconomics and EconometricsMains electricityViscosity solutionDynamic demand managementPopulationDistributional solutionsInterval (mathematics)law.inventionSettore ING-INF/04 - AutomaticalawControl theoryEconomicseducationeducation.field_of_studyApplied MathematicsComputer Graphics and Computer-Aided DesignThermostatMean field gameComputer Science ApplicationsPower (physics)Computational MathematicsComputational Theory and MathematicsTerminal (electronics)Dynamic demandSettore MAT/09 - Ricerca OperativaGame theoryMathematical economics
researchProduct