OPERATOR VALUED STOCHASTIC CONTROL IN FOCK SPACE.-WITH APPLICATIONS TO ORBIT TRACKING AND NOISE FILTERING

Abstract. The control process that minimizes the quadratic per-formance functional associated with a quantum system whose evolu-tion is described by a Hudson-Parthasarathy type stochastic differen-tial 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 soIution to an associated optimal trajectory problem is also obtained. 1. Introduction to stochastic calculus in Fock space. Using the ideas of the fundamental paper of Accardi et al. [I], Hudson and Parthasarathy construc-ted in [ll] a simple noncommutative stochastic calculus in boson Fock space that was shown to include the classical Brownian motion and Poisson proces-ses. Their theory has been parficularly useful in the study of phenomena relate