86 research outputs found
Smart grids as distributed learning control
The topic of smart grids has received a lot of attention but from a scientific point of view it is a highly imprecise concept. This paper attempts to describe what could ultimately work as a control process to fulfill the aims usually stated for such grids without throwing away some important principles established by the pioneers in power system control. In modern terms, we need distributed (or multi-agent) learning control which is suggested to work with a certain consensus mechanism which appears to leave room for achieving cyber-physical security, robustness and performance goals. © 2012 IEEE.published_or_final_versio
Passive Dynamics in Mean Field Control
Mean-field models are a popular tool in a variety of fields. They provide an
understanding of the impact of interactions among a large number of particles
or people or other "self-interested agents", and are an increasingly popular
tool in distributed control.
This paper considers a particular randomized distributed control architecture
introduced in our own recent work. In numerical results it was found that the
associated mean-field model had attractive properties for purposes of control.
In particular, when viewed as an input-output system, its linearization was
found to be minimum phase.
In this paper we take a closer look at the control model. The results are
summarized as follows:
(i) The Markov Decision Process framework of Todorov is extended to
continuous time models, in which the "control cost" is based on relative
entropy. This is the basis of the construction of a family of controlled
Markovian generators.
(ii) A decentralized control architecture is proposed in which each agent
evolves as a controlled Markov process. A central authority broadcasts a common
control signal to each agent. The central authority chooses this signal based
on an aggregate scalar output of the Markovian agents.
(iii) Provided the control-free system is a reversible Markov process, the
following identity holds for the linearization, where the right hand side
denotes the power spectral density for the output of any one of the individual
(control-free) Markov processes.Comment: To appear IEEE CDC, 201
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
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
Individual risk in mean-field control models for decentralized control, with application to automated demand response
Flexibility of energy consumption can be harnessed for the purposes of
ancillary services in a large power grid. In prior work by the authors a
randomized control architecture is introduced for individual loads for this
purpose. In examples it is shown that the control architecture can be designed
so that control of the loads is easy at the grid level: Tracking of a balancing
authority reference signal is possible, while ensuring that the quality of
service (QoS) for each load is acceptable on average. The analysis was based on
a mean field limit (as the number of loads approaches infinity), combined with
an LTI-system approximation of the aggregate nonlinear model. This paper
examines in depth the issue of individual risk in these systems. The main
contributions of the paper are of two kinds:
Risk is modeled and quantified:
(i) The average performance is not an adequate measure of success. It is
found empirically that a histogram of QoS is approximately Gaussian, and
consequently each load will eventually receive poor service.
(ii) The variance can be estimated from a refinement of the LTI model that
includes a white-noise disturbance; variance is a function of the randomized
policy, as well as the power spectral density of the reference signal.
Additional local control can eliminate risk:
(iii) The histogram of QoS is truncated through this local control, so that
strict bounds on service quality are guaranteed.
(iv) This has insignificant impact on the grid-level performance, beyond a
modest reduction in capacity of ancillary service.Comment: Publication without appendix to appear in the 53rd IEEE Conf. on
Decision and Control, December, 201
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
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