A certainty equivalence control with a nonlinear filter in the feedback loop

The problem of control of a linear stochastic system observed by both linear and hard limited measurements is considered. The control used is the LQG or deterministic linear feedback control where the state estimate is generated by a recursive nonlinear filter. It is shown that the feedback nature of the control induces a natural probing which activates the filter. The results of this feedback system with a nonlinear filter in the feedback loop is compated to a system with an extended Kalman filter in the feedback loop. The state estimation accuracy is also compared to the system without a control to demonstrate how the control activates the nonlinear filter.