OPERATOR VALUED STOCHASTIC CONTROL IN FOCK SPACE WITH
APPLICATIONS TO ORBIT TRACKING AND NOISE FILTERING
Abstract: The control process that minimizes the quadratic performance functional associated
with a quantum system whose evolution is described by a Hudson-Parthasarathy type
stochastic differential equation in Fock space is explicitly computed. A “noisy”
infinite-dimensional Riccati equation appears for the first time and it is shown to have a
unique solution. The solution to the control problem is used to derive the Fock space
analogue of the Bucy-Kalman filter. The solution to an associated optimal trajectory problem
is also obtained.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -