On certainty equivalence in linear-quadratic control problems with nonlinear measurements

The certainty equivalence property is investigated in the framework of stochastic control problems with linear continuous time state models and a quadratic cost. The objective is to show that some nonlinear measurements admit the certainty equivalence property to hold with only mild assumptions on stochastic properties (e.g., square integrability) of the initial state, the process noise and the measurements noise. As the classes of nonlinear measurements, we consider the additive type, the multiplicative type, the continuous time version of Curry's type and the data processor.