On A Class of Stochastic Bang-Bang Continuous Time Control Problems.

摘要

The report deals with the optimal control of a class of stochastic,continuous time system with noisy observations on a finite time interval. The evolution of the state of the system as well as the observation process are described by linear stochastic differential equations. The optimal control process is required to be bounded in magnitude and to depend only on the data available,the optimality being taken in the mean square sense. The control constraints make the overall problem nonlinear. In addition to existence as well as necessary and/or sufficient conditions for optimality,the author obtains an explicite characterization of the optimal control;it is shown that the optimal control is of bang-bang type and is a function of the Kalman estimate of the state. (Modified author abstract)