189 research outputs found
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
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
State Estimation for the Individual and the Population in Mean Field Control with Application to Demand Dispatch
This paper concerns state estimation problems in a mean field control
setting. In a finite population model, the goal is to estimate the joint
distribution of the population state and the state of a typical individual. The
observation equations are a noisy measurement of the population.
The general results are applied to demand dispatch for regulation of the
power grid, based on randomized local control algorithms. In prior work by the
authors it has been shown that local control can be carefully designed so that
the aggregate of loads behaves as a controllable resource with accuracy
matching or exceeding traditional sources of frequency regulation. The
operational cost is nearly zero in many cases.
The information exchange between grid and load is minimal, but it is assumed
in the overall control architecture that the aggregate power consumption of
loads is available to the grid operator. It is shown that the Kalman filter can
be constructed to reduce these communication requirements,Comment: To appear, IEEE Trans. Auto. Control. Preliminary version appeared in
the 54rd IEEE Conference on Decision and Control, 201
Speeding up Glauber Dynamics for Random Generation of Independent Sets
The maximum independent set (MIS) problem is a well-studied combinatorial
optimization problem that naturally arises in many applications, such as
wireless communication, information theory and statistical mechanics.
MIS problem is NP-hard, thus many results in the literature focus on fast
generation of maximal independent sets of high cardinality. One possibility is
to combine Gibbs sampling with coupling from the past arguments to detect
convergence to the stationary regime. This results in a sampling procedure with
time complexity that depends on the mixing time of the Glauber dynamics Markov
chain.
We propose an adaptive method for random event generation in the Glauber
dynamics that considers only the events that are effective in the coupling from
the past scheme, accelerating the convergence time of the Gibbs sampling
algorithm
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