State Estimation for the Individual and the Population in Mean Field Control with Application to Demand Dispatch
Résumé
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, and to provide the
grid operator with accurate estimates of the mean and variance
of quality of service (QoS) for an individual load.