2,093 research outputs found
Hypergraph conditions for the solvability of the ergodic equation for zero-sum games
The ergodic equation is a basic tool in the study of mean-payoff stochastic
games. Its solvability entails that the mean payoff is independent of the
initial state. Moreover, optimal stationary strategies are readily obtained
from its solution. In this paper, we give a general sufficient condition for
the solvability of the ergodic equation, for a game with finite state space but
arbitrary action spaces. This condition involves a pair of directed hypergraphs
depending only on the ``growth at infinity'' of the Shapley operator of the
game. This refines a recent result of the authors which only applied to games
with bounded payments, as well as earlier nonlinear fixed point results for
order preserving maps, involving graph conditions.Comment: 6 pages, 1 figure, to appear in Proc. 54th IEEE Conference on
Decision and Control (CDC 2015
A Quantum Langevin Formulation of Risk-Sensitive Optimal Control
In this paper we formulate a risk-sensitive optimal control problem for
continuously monitored open quantum systems modelled by quantum Langevin
equations. The optimal controller is expressed in terms of a modified
conditional state, which we call a risk-sensitive state, that represents
measurement knowledge tempered by the control purpose. One of the two
components of the optimal controller is dynamic, a filter that computes the
risk-sensitive state.
The second component is an optimal control feedback function that is found by
solving the dynamic programming equation. The optimal controller can be
implemented using classical electronics.
The ideas are illustrated using an example of feedback control of a two-level
atom
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