Abstract
Abstract The problem of the estimation and observation control is considered for the stochastic system with a state-estimation dependent noise in observations. The optimal estimation in the class of linear filters was obtained and the separation principle for the linear-quadratic optimization problem was also proved. It gives the opportunity to solve simultaneously the control problem for the process and observations. This new problem belongs to a class of singular control problems and can be solved by standard methods of impulsive control theory.
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