166,159 research outputs found
Dynamic demand and mean-field games
Within the realm of smart buildings and smart cities,
dynamic response management is playing an ever-increasing
role thus attracting the attention of scientists from different
disciplines. Dynamic demand response management involves a
set of operations aiming at decentralizing the control of loads
in large and complex power networks. Each single appliance
is fully responsive and readjusts its energy demand to the
overall network load. A main issue is related to mains frequency
oscillations resulting from an unbalance between supply and
demand. In a nutshell, this paper contributes to the topic by
equipping each signal consumer with strategic insight. In particular,
we highlight three main contributions and a few other minor
contributions. First, we design a mean-field game for a population
of thermostatically controlled loads (TCLs), study the mean-field
equilibrium for the deterministic mean-field game and investigate
on asymptotic stability for the microscopic dynamics. Second, we
extend the analysis and design to uncertain models which involve
both stochastic or deterministic disturbances. This leads to robust
mean-field equilibrium strategies guaranteeing stochastic and
worst-case stability, respectively. Minor contributions involve the
use of stochastic control strategies rather than deterministic, and
some numerical studies illustrating the efficacy of the proposed
strategies
Crowd-Averse Robust Mean-Field Games: Approximation via State Space Extension
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 crosscoupling mean-field term measuring the congestion resulting from the collective behavior, which motivates the term “crowdaverse”. 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 the problem in its abstract formulation, we illustrate the paradigm of robust mean-field games. Main contributions involve first the formulation of the problem as a robust mean-field game; second, the development of a new approximate solution approach based on the extension of the state space; third, a relaxation method to minimize the approximation error. Further results are provided for the scalar case, for which we establish performance bounds, and analyze stochastic stability of both the microscopic and the macroscopic dynamics
A mirror descent approach for Mean Field Control applied to Demande-Side management
We consider a finite-horizon Mean Field Control problem for Markovian models.
The objective function is composed of a sum of convex and Lipschitz functions
taking their values on a space of state-action distributions. We introduce an
iterative algorithm which we prove to be a Mirror Descent associated with a
non-standard Bregman divergence, having a convergence rate of order 1/ \sqrt
K. It requires the solution of a simple dynamic programming problem at each
iteration. We compare this algorithm with learning methods for Mean Field Games
after providing a reformulation of our control problem as a game problem. These
theoretical contributions are illustrated with numerical examples applied to a
demand-side management problem for power systems aimed at controlling the
average power consumption profile of a population of flexible devices
contributing to the power system balance
Mean-Field-Type Games in Engineering
A mean-field-type game is a game in which the instantaneous payoffs and/or
the state dynamics functions involve not only the state and the action profile
but also the joint distributions of state-action pairs. This article presents
some engineering applications of mean-field-type games including road traffic
networks, multi-level building evacuation, millimeter wave wireless
communications, distributed power networks, virus spread over networks, virtual
machine resource management in cloud networks, synchronization of oscillators,
energy-efficient buildings, online meeting and mobile crowdsensing.Comment: 84 pages, 24 figures, 183 references. to appear in AIMS 201
Decentralized Convergence to Nash Equilibria in Constrained Deterministic Mean Field Control
This paper considers decentralized control and optimization methodologies for
large populations of systems, consisting of several agents with different
individual behaviors, constraints and interests, and affected by the aggregate
behavior of the overall population. For such large-scale systems, the theory of
aggregative and mean field games has been established and successfully applied
in various scientific disciplines. While the existing literature addresses the
case of unconstrained agents, we formulate deterministic mean field control
problems in the presence of heterogeneous convex constraints for the individual
agents, for instance arising from agents with linear dynamics subject to convex
state and control constraints. We propose several model-free feedback
iterations to compute in a decentralized fashion a mean field Nash equilibrium
in the limit of infinite population size. We apply our methods to the
constrained linear quadratic deterministic mean field control problem and to
the constrained mean field charging control problem for large populations of
plug-in electric vehicles.Comment: IEEE Trans. on Automatic Control (cond. accepted
Mean Field Equilibrium in Dynamic Games with Complementarities
We study a class of stochastic dynamic games that exhibit strategic
complementarities between players; formally, in the games we consider, the
payoff of a player has increasing differences between her own state and the
empirical distribution of the states of other players. Such games can be used
to model a diverse set of applications, including network security models,
recommender systems, and dynamic search in markets. Stochastic games are
generally difficult to analyze, and these difficulties are only exacerbated
when the number of players is large (as might be the case in the preceding
examples).
We consider an approximation methodology called mean field equilibrium to
study these games. In such an equilibrium, each player reacts to only the long
run average state of other players. We find necessary conditions for the
existence of a mean field equilibrium in such games. Furthermore, as a simple
consequence of this existence theorem, we obtain several natural monotonicity
properties. We show that there exist a "largest" and a "smallest" equilibrium
among all those where the equilibrium strategy used by a player is
nondecreasing, and we also show that players converge to each of these
equilibria via natural myopic learning dynamics; as we argue, these dynamics
are more reasonable than the standard best response dynamics. We also provide
sensitivity results, where we quantify how the equilibria of such games move in
response to changes in parameters of the game (e.g., the introduction of
incentives to players).Comment: 56 pages, 5 figure
- …