2,264 research outputs found
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
Continuous-time integral dynamics for Aggregative Game equilibrium seeking
In this paper, we consider continuous-time semi-decentralized dynamics for
the equilibrium computation in a class of aggregative games. Specifically, we
propose a scheme where decentralized projected-gradient dynamics are driven by
an integral control law. To prove global exponential convergence of the
proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov
function argument. We derive a sufficient condition for global convergence that
we position within the recent literature on aggregative games, and in
particular we show that it improves on established results
Regularized Jacobi iteration for decentralized convex optimization with separable constraints
We consider multi-agent, convex optimization programs subject to separable
constraints, where the constraint function of each agent involves only its
local decision vector, while the decision vectors of all agents are coupled via
a common objective function. We focus on a regularized variant of the so called
Jacobi algorithm for decentralized computation in such problems. We first
consider the case where the objective function is quadratic, and provide a
fixed-point theoretic analysis showing that the algorithm converges to a
minimizer of the centralized problem. Moreover, we quantify the potential
benefits of such an iterative scheme by comparing it against a scaled projected
gradient algorithm. We then consider the general case and show that all limit
points of the proposed iteration are optimal solutions of the centralized
problem. The efficacy of the proposed algorithm is illustrated by applying it
to the problem of optimal charging of electric vehicles, where, as opposed to
earlier approaches, we show convergence to an optimal charging scheme for a
finite, possibly large, number of vehicles
A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games
We address the generalized aggregative equilibrium seeking problem for
noncooperative agents playing average aggregative games with affine coupling
constraints. First, we use operator theory to characterize the generalized
aggregative equilibria of the game as the zeros of a monotone set-valued
operator. Then, we massage the Douglas-Rachford splitting to solve the monotone
inclusion problem and derive a single layer, semi-decentralized algorithm whose
global convergence is guaranteed under mild assumptions. The potential of the
proposed Douglas-Rachford algorithm is shown on a simplified resource
allocation game, where we observe faster convergence with respect to
forward-backward algorithms.Comment: arXiv admin note: text overlap with arXiv:1803.1044
Battery Capacity of Deferrable Energy Demand
We investigate the ability of a homogeneous collection of deferrable energy
loads to behave as a battery; that is, to absorb and release energy in a
controllable fashion up to fixed and predetermined limits on volume, charge
rate and discharge rate. We derive bounds on the battery capacity that can be
realized and show that there are fundamental trade-offs between battery
parameters. By characterizing the state trajectories under scheduling policies
that emulate two illustrative batteries, we show that the trade-offs occur
because the states that allow the loads to absorb and release energy at high
aggregate rates are conflicting
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