5 research outputs found
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
Partially Observed Discrete-Time Risk-Sensitive Mean Field Games
In this paper, we consider discrete-time partially observed mean-field games
with the risk-sensitive optimality criterion. We introduce risk-sensitivity
behaviour for each agent via an exponential utility function. In the game
model, each agent is weakly coupled with the rest of the population through its
individual cost and state dynamics via the empirical distribution of states. We
establish the mean-field equilibrium in the infinite-population limit using the
technique of converting the underlying original partially observed stochastic
control problem to a fully observed one on the belief space and the dynamic
programming principle. Then, we show that the mean-field equilibrium policy,
when adopted by each agent, forms an approximate Nash equilibrium for games
with sufficiently many agents. We first consider finite-horizon cost function,
and then, discuss extension of the result to infinite-horizon cost in the
next-to-last section of the paper.Comment: 29 pages. arXiv admin note: substantial text overlap with
arXiv:1705.02036, arXiv:1808.0392